TSTP Solution File: SWW289+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW289+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n022.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 23:21:52 EDT 2022
% Result : Timeout 300.05s 300.50s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWW289+1 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.12 % Command : bliksem %s
% 0.12/0.32 % Computer : n022.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Mon Jun 6 07:50:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.93/1.56 *** allocated 10000 integers for termspace/termends
% 0.93/1.56 *** allocated 10000 integers for clauses
% 0.93/1.56 *** allocated 10000 integers for justifications
% 0.93/1.56 *** allocated 15000 integers for termspace/termends
% 0.93/1.56 *** allocated 22500 integers for termspace/termends
% 0.93/1.56 *** allocated 33750 integers for termspace/termends
% 0.93/1.56 Bliksem 1.12
% 0.93/1.56
% 0.93/1.56
% 0.93/1.56 Automatic Strategy Selection
% 0.93/1.56
% 0.93/1.56 *** allocated 50625 integers for termspace/termends
% 0.93/1.56 *** allocated 75937 integers for termspace/termends
% 0.93/1.56 *** allocated 113905 integers for termspace/termends
% 0.93/1.56
% 0.93/1.56 Clauses:
% 0.93/1.56
% 0.93/1.56 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.93/1.56 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ), v_p
% 0.93/1.56 , v_q ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.93/1.56 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.93/1.56 ) }.
% 0.93/1.56 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.93/1.56 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.93/1.56 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.93/1.56 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.93/1.56 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.93/1.56 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.93/1.56 ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.93/1.56 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.93/1.56 Z, T ) }.
% 0.93/1.56 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.93/1.56 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), X ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.93/1.56 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.93/1.56 tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 0.93/1.56 Y ) ), X ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.93/1.56 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.93/1.56 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.93/1.56 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.93/1.56 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.93/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha1( X
% 0.93/1.56 , Y, T ) }.
% 0.93/1.56 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.93/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha27( X
% 0.93/1.56 , Y, Z, T ) }.
% 0.93/1.56 { ! class_Fields_Ofield( X ), ! alpha1( X, Y, T ), ! alpha27( X, Y, Z, T )
% 0.93/1.56 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 0.93/1.56 ( X, T, Z ), Y ) }.
% 0.93/1.56 { ! alpha27( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.56 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.93/1.56 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha27( X, Y, Z, T ) }.
% 0.93/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha27( X
% 0.93/1.56 , Y, Z, T ) }.
% 0.93/1.56 { ! alpha1( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { Z = c_Groups_Ozero__class_Ozero( X ), alpha1( X, Y, Z ) }.
% 0.93/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha1( X
% 0.93/1.56 , Y, Z ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.93/1.56 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.93/1.56 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.93/1.56 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.93/1.56 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.93/1.56 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.93/1.56 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 0.93/1.56 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.93/1.56 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.93/1.56 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.93/1.56 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.93/1.56 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.56 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.93/1.56 ), X ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.93/1.56 { c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) = hAPP(
% 0.93/1.56 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) ), X ) }.
% 0.93/1.56 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.93/1.56 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.93/1.56 ), Y ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.93/1.56 tc_Complex_Ocomplex ) ) ) ), X ) = hAPP( c_Polynomial_Opoly(
% 0.93/1.56 tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.93/1.56 tc_Complex_Ocomplex ) ) ), X ) }.
% 0.93/1.56 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.93/1.56 tc_Complex_Ocomplex, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 0.93/1.56 ( tc_Complex_Ocomplex ) ) ) ), X ) = Y }.
% 0.93/1.56 { Y = hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.93/1.56 tc_Complex_Ocomplex, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 0.93/1.56 ( tc_Complex_Ocomplex ) ) ) ), X ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.93/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 0.93/1.56 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.93/1.56 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.93/1.56 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.93/1.56 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.93/1.56 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.93/1.56 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.93/1.56 tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.93/1.56 ) ), X ) = hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.93/1.56 ), X ) }.
% 0.93/1.56 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.93/1.56 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.93/1.56 tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.93/1.56 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.93/1.56 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.56 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 0.93/1.56 X, T, Z ), Y ) }.
% 0.93/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.93/1.56 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.93/1.56 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 0.93/1.56 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.93/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.93/1.56 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 0.93/1.56 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.93/1.56 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 0.93/1.56 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.56 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.93/1.56 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.93/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.93/1.56 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.93/1.56 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.93/1.56 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.93/1.56 ) }.
% 0.93/1.56 { X = hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.93/1.56 tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 0.93/1.56 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.93/1.56 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.93/1.56 tc_Complex_Ocomplex ) ) ) ) ), X ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.93/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.93/1.56 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.93/1.56 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.93/1.56 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.93/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 0.93/1.56 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { ! class_Groups_Ozero( X ), ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero
% 0.93/1.56 ( tc_Polynomial_Opoly( X ) ) ) ), hBOOL( hAPP( Y, skol2( Z, Y ) ) ),
% 0.93/1.56 hBOOL( hAPP( Y, T ) ) }.
% 0.93/1.56 { ! class_Groups_Ozero( X ), ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero
% 0.93/1.56 ( tc_Polynomial_Opoly( X ) ) ) ), ! hBOOL( hAPP( Y, c_Polynomial_OpCons(
% 0.93/1.56 X, skol20( X, Y ), skol2( X, Y ) ) ) ), hBOOL( hAPP( Y, Z ) ) }.
% 0.93/1.56 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.56 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { ! class_Groups_Ozero( X ), !
% 0.93/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ),
% 0.93/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.56 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.93/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.56 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.93/1.56 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.93/1.56 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.93/1.56 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.93/1.56 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.93/1.56 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.93/1.56 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.93/1.56 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.93/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.93/1.56 T, Y ), Z = Y }.
% 0.93/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.93/1.56 T, Y ) }.
% 0.93/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.93/1.56 Y, Z ), T = Y }.
% 0.93/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.93/1.56 Y, Z ) }.
% 0.93/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.93/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.93/1.56 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.93/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.93/1.56 T, Y ), Z = Y }.
% 0.93/1.56 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.93/1.56 T, Y ), Z = Y }.
% 0.93/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.93/1.56 Y, T ), Z = Y }.
% 0.93/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.93/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.93/1.56 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.93/1.56 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.93/1.56 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.93/1.56 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.93/1.56 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.93/1.56 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.93/1.56 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.93/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.93/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 0.93/1.56 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.93/1.56 , Y ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.93/1.56 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ) ) }.
% 0.93/1.56 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.93/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.93/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.93/1.56 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.93/1.56 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.93/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.93/1.56 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.93/1.56 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.93/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.93/1.56 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.93/1.56 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.93/1.56 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.93/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.93/1.56 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.93/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.93/1.56 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.93/1.56 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.93/1.56 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 0.93/1.56 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 0.93/1.56 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.93/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.93/1.56 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.93/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 0.93/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 0.93/1.56 c_Polynomial_OpCons( X, T,
% 0.93/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 0.93/1.56 .
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.93/1.56 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.93/1.56 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 0.93/1.56 }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.93/1.56 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.93/1.56 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 0.93/1.56 ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 0.93/1.56 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 0.93/1.56 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 0.93/1.56 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 0.93/1.56 , Y ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), !
% 0.93/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 0.93/1.56 ( tc_Polynomial_Opoly( X ) ),
% 0.93/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.93/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.93/1.56 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.93/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.93/1.56 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.93/1.56 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.93/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.56 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.93/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.93/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.93/1.56 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 0.93/1.56 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.93/1.56 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.93/1.56 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 0.93/1.56 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.93/1.56 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.93/1.56 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.93/1.56 X ) }.
% 0.93/1.56 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.93/1.56 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 0.93/1.56 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.93/1.56 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.93/1.56 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.93/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.93/1.56 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.93/1.56 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.93/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 0.93/1.56 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 0.93/1.56 .
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.93/1.56 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.93/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.93/1.56 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 0.93/1.56 .
% 0.93/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 0.93/1.56 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.56 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 0.93/1.56 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Nat_Onat ) ) }.
% 0.93/1.56 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.93/1.56 tc_Nat_Onat ), X ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.93/1.56 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.93/1.56 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.93/1.56 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.93/1.56 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.93/1.56 ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.56 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.93/1.56 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.93/1.56 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.93/1.56 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.93/1.56 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.93/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.93/1.56 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.56 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.93/1.56 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.93/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.93/1.56 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.93/1.56 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.93/1.56 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.93/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.93/1.56 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.93/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.93/1.56 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.93/1.56 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.93/1.56 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.93/1.56 ( X, Y ) ) }.
% 0.93/1.56 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.56 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.93/1.56 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.56 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.93/1.56 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.93/1.56 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.93/1.56 ) ), Y ) }.
% 0.93/1.56 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.93/1.56 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.93/1.56 ( X, Y ) ) }.
% 0.93/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.93/1.56 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.93/1.56 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.93/1.56 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.93/1.56 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.56 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.56 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.93/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.93/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.93/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.93/1.56 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.93/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.93/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.93/1.56 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.93/1.56 ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.93/1.56 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.93/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.93/1.56 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.93/1.56 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.93/1.56 ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.93/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.93/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.56 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.93/1.56 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.93/1.56 ) }.
% 0.93/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.93/1.56 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.93/1.56 ), ! U = T }.
% 0.93/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.93/1.56 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.93/1.56 ), ! Z = Y }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.93/1.56 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.93/1.56 ) ), Z ) }.
% 0.93/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.93/1.56 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.93/1.56 ), U = Z, T = Y }.
% 0.93/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.93/1.56 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.93/1.56 ) }.
% 0.93/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.93/1.56 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.93/1.56 ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.93/1.56 = Y }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.93/1.56 = Y }.
% 0.93/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.93/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.93/1.56 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.93/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.93/1.56 = Y }.
% 0.93/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.93/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.93/1.56 ) }.
% 0.93/1.56 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.93/1.56 ) }.
% 0.93/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.93/1.56 ( X ) }.
% 0.93/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.56 , Y ) }.
% 0.93/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.93/1.56 = Y }.
% 0.93/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.93/1.56 ) }.
% 0.93/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.56 Z, Y ) ) = Y }.
% 0.93/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.93/1.56 Y ) ) = Y }.
% 0.93/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.93/1.56 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.93/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.93/1.56 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 0.93/1.56 , Z, Y ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.93/1.56 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 0.93/1.56 ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.93/1.56 , Y ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.93/1.56 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.93/1.56 ) }.
% 0.93/1.56 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.56 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.56 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.56 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.93/1.56 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.56 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.93/1.56 ) ), T ), Y ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.93/1.56 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.56 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.93/1.56 = Y }.
% 0.93/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.93/1.56 = Y }.
% 0.93/1.56 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.93/1.56 = Y }.
% 0.93/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.93/1.56 = Y }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.93/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 0.93/1.56 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.93/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 0.93/1.56 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.93/1.56 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.56 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.93/1.56 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 0.93/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.93/1.56 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.93/1.56 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.93/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.93/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.93/1.56 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.93/1.56 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.93/1.56 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.93/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.93/1.56 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.93/1.56 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 0.93/1.56 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 0.93/1.56 .
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.93/1.56 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 0.93/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 0.93/1.56 ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.93/1.56 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.56 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.93/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.93/1.56 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.93/1.56 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.93/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.93/1.56 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.93/1.56 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.93/1.56 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.93/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.93/1.56 ) ) }.
% 0.93/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.93/1.56 X ) }.
% 0.93/1.56 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.56 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.93/1.56 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.93/1.56 ( X, Y ) }.
% 0.93/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.93/1.56 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.56 Z ) = Y }.
% 0.93/1.56 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.93/1.56 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.56 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.93/1.56 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.93/1.56 }.
% 0.93/1.56 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.93/1.56 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.93/1.56 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.93/1.56 }.
% 0.93/1.56 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 0.93/1.56 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.93/1.56 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.56 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.93/1.56 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.93/1.56 }.
% 0.93/1.56 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.93/1.56 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.93/1.56 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.93/1.56 }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.93/1.56 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 0.93/1.56 Y ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.93/1.56 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.93/1.56 , Y ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.93/1.56 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 0.93/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.93/1.56 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.93/1.56 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.93/1.56 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.93/1.56 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.93/1.56 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.93/1.56 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.93/1.56 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.56 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.93/1.56 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.93/1.56 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.93/1.56 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.93/1.56 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.93/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.93/1.56 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.93/1.56 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.93/1.56 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.93/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.93/1.56 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.93/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.93/1.56 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.93/1.56 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.93/1.56 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.93/1.56 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.93/1.56 hAPP( Z, skol3( U, W, Z ) ) ) }.
% 0.93/1.56 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.93/1.57 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol3( X
% 0.93/1.57 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.93/1.57 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 0.93/1.57 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol21( X,
% 0.93/1.57 Y, Z ) ) ) ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.57 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.93/1.57 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.93/1.57 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.93/1.57 ( X, Z ) }.
% 0.93/1.57 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.57 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.57 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.93/1.57 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.93/1.57 ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.57 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.93/1.57 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.93/1.57 ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.57 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 0.93/1.57 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.93/1.57 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.93/1.57 Y ) ) ), Y ) }.
% 0.93/1.57 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.93/1.57 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 0.93/1.57 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.93/1.57 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.93/1.57 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.93/1.57 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.93/1.57 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.93/1.57 Y ) ) ), Y ) }.
% 0.93/1.57 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.57 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.93/1.57 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.93/1.57 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.93/1.57 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.57 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.93/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.93/1.57 tc_Nat_Onat ) }.
% 0.93/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.93/1.57 tc_Nat_Onat ) }.
% 0.93/1.57 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.93/1.57 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.93/1.57 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.93/1.57 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.93/1.57 tc_Nat_Onat ) ) = Y }.
% 0.93/1.57 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.93/1.57 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.93/1.57 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.93/1.57 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.93/1.57 , Y ), X ) }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.93/1.57 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.93/1.57 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.93/1.57 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.93/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.93/1.57 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.93/1.57 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.93/1.57 .
% 0.93/1.57 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.93/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.93/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.93/1.57 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.93/1.57 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.93/1.57 .
% 0.93/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.93/1.57 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.93/1.57 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.93/1.57 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.57 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.93/1.57 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.57 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.57 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.93/1.57 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.93/1.57 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Nat_Onat, Z, Y ) ) }.
% 0.93/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.93/1.57 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.93/1.57 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.93/1.57 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.93/1.57 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.57 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.93/1.57 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.57 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.93/1.57 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.93/1.57 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.93/1.57 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.93/1.57 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.93/1.57 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.93/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.93/1.57 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.93/1.57 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.93/1.57 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.93/1.57 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ), X ) = X }.
% 0.93/1.57 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ) ) = X }.
% 0.93/1.57 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.93/1.57 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.93/1.57 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.93/1.57 { ! c_Nat_OSuc( X ) = X }.
% 0.93/1.57 { ! X = c_Nat_OSuc( X ) }.
% 0.93/1.57 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.93/1.57 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.93/1.57 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.93/1.57 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.93/1.57 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.93/1.57 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.93/1.57 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.93/1.57 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha2( X, Y ), Y = X }
% 0.93/1.57 .
% 0.93/1.57 { ! alpha2( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! alpha2( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! alpha2( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Nat_Onat, X, Y ), alpha2( X, Y ) }.
% 0.93/1.57 { ! alpha3( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! alpha3( X, Y ), ! Y = X }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha3( X, Y ) }
% 0.93/1.57 .
% 0.93/1.57 { ! alpha3( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! alpha3( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Nat_Onat, X, Y ), alpha3( X, Y ) }.
% 0.93/1.57 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.93/1.57 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Nat_Onat, Y, X ), Y = X }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.93/1.57 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Nat_Onat, Y, Z ) }.
% 0.93/1.57 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Nat_Onat, Y, Z ) }.
% 0.93/1.57 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Nat_Onat, Z, Y ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 0.93/1.57 , Z ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 0.93/1.57 Z, Y ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Nat_Onat, Y, Z ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Nat_Onat, Z, Y ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 0.93/1.57 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.93/1.57 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.93/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.93/1.57 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 0.93/1.57 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 0.93/1.57 X, Z ), Y ) ) }.
% 0.93/1.57 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.93/1.57 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 0.93/1.57 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.93/1.57 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.93/1.57 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.93/1.57 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.93/1.57 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.93/1.57 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.93/1.57 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha4( X, Y ), alpha28( X
% 0.93/1.57 , Y ) }.
% 0.93/1.57 { ! alpha4( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.93/1.57 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.57 { ! alpha28( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.93/1.57 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.57 { ! alpha28( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! alpha28( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ) ) }.
% 0.93/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha28( X, Y ) }.
% 0.93/1.57 { ! alpha4( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ) ) }.
% 0.93/1.57 { ! alpha4( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha4( X, Y ) }.
% 0.93/1.57 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha5( X, Y ), alpha29
% 0.93/1.57 ( X, Y ) }.
% 0.93/1.57 { ! alpha5( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.93/1.57 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! alpha29( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.93/1.57 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! alpha29( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! alpha29( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ) ) }.
% 0.93/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha29( X, Y ) }.
% 0.93/1.57 { ! alpha5( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ) ) }.
% 0.93/1.57 { ! alpha5( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha5( X, Y ) }.
% 0.93/1.57 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.93/1.57 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.57 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.93/1.57 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.93/1.57 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.57 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.93/1.57 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.93/1.57 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.93/1.57 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.93/1.57 c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.57 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.93/1.57 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.93/1.57 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.93/1.57 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.93/1.57 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.57 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.93/1.57 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.93/1.57 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.93/1.57 .
% 0.93/1.57 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.93/1.57 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.93/1.57 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ) }.
% 0.93/1.57 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.93/1.57 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.93/1.57 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.93/1.57 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.93/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.93/1.57 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.93/1.57 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.93/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Int_Oint, Z, X ) }.
% 0.93/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.93/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 0.93/1.57 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 0.93/1.57 ) }.
% 0.93/1.57 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.93/1.57 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.57 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.93/1.57 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.57 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.93/1.57 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.93/1.57 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Nat_Onat, Z, X ) }.
% 0.93/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.93/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 0.93/1.57 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 0.93/1.57 ) }.
% 0.93/1.57 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.93/1.57 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( X ) }.
% 0.93/1.57 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.93/1.57 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.93/1.57 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.93/1.57 = c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.93/1.57 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.93/1.57 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.93/1.57 tc_Nat_Onat ) ) = Y }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.57 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.93/1.57 X ) ) }.
% 0.93/1.57 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.93/1.57 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.93/1.57 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.93/1.57 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.93/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.93/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.93/1.57 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.93/1.57 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.93/1.57 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.93/1.57 .
% 0.93/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.93/1.57 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.93/1.57 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.93/1.57 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 0.93/1.57 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.93/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 0.93/1.57 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 0.93/1.57 ) ) }.
% 0.93/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.93/1.57 , Z ), X ) ), T ) ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Int_Oint, U, T ) ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Int_Oint, Y, X ) }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.93/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.93/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.93/1.57 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 0.93/1.57 .
% 0.93/1.57 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.93/1.57 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.93/1.57 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.93/1.57 ) ) }.
% 0.93/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.93/1.57 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.93/1.57 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.93/1.57 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.93/1.57 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.93/1.57 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.93/1.57 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.57 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.57 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.93/1.57 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.93/1.57 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.57 { ! alpha6( X, Y ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.93/1.57 tc_Complex_Ocomplex ), Y, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.57 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), X ), c_Polynomial_Odegree(
% 0.93/1.57 tc_Complex_Ocomplex, Y ) ) ), alpha30( X, Y ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y
% 0.93/1.57 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.93/1.57 tc_Complex_Ocomplex ) ), X ), c_Polynomial_Odegree( tc_Complex_Ocomplex,
% 0.93/1.57 Y ) ) ), alpha6( X, Y ) }.
% 0.93/1.57 { ! alpha30( X, Y ), alpha6( X, Y ) }.
% 0.93/1.57 { ! alpha30( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.93/1.57 tc_Complex_Ocomplex ) ) }.
% 0.93/1.57 { ! alpha30( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.93/1.57 tc_Complex_Ocomplex ) ) }.
% 0.93/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.93/1.57 tc_Complex_Ocomplex ) ), ! X = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), alpha30( X, Y ) }.
% 0.93/1.57 { ! alpha6( X, Y ), ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), Z
% 0.93/1.57 ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.93/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), Z ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.93/1.57 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), skol4( Z, Y ) ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), alpha6( X, Y ) }.
% 0.93/1.57 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol4( X, Y ) ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), alpha6( X, Y ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.93/1.57 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.93/1.57 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.93/1.57 { c_Nat_Onat_Onat__size( c_Nat_OSuc( X ) ) = c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Nat_Onat, c_Nat_Onat_Onat__size( X ), c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.93/1.57 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.93/1.57 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.93/1.57 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 0.93/1.57 ( X ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 0.93/1.57 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.93/1.57 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.93/1.57 ( tc_Nat_Onat ) ) ) ) }.
% 0.93/1.57 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.93/1.57 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.93/1.57 c_Polynomial_Odegree( X, Y ) ), ! c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Polynomial_Opoly( X ), Y, Z ), Z = Y }.
% 0.93/1.57 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.93/1.57 ( tc_Int_Oint ) }.
% 0.93/1.57 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.93/1.57 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.93/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Int_Oint ), X ) = X }.
% 0.93/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Int_Oint ) ) = X }.
% 0.93/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.93/1.57 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.93/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.93/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.93/1.57 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.93/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.93/1.57 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.93/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.93/1.57 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.93/1.57 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.93/1.57 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.93/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.93/1.57 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.93/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.93/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.93/1.57 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 0.93/1.57 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.93/1.57 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.93/1.57 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.93/1.57 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.93/1.57 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 0.93/1.57 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.93/1.57 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 0.93/1.57 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 0.93/1.57 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 0.93/1.57 c_Polynomial_Ocoeff( X, Y ) }.
% 0.93/1.57 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 0.93/1.57 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 0.93/1.57 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol5( X
% 0.93/1.57 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol5( X, Y, Z ) ), Z = Y
% 0.93/1.57 }.
% 0.93/1.57 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.93/1.57 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.93/1.57 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.93/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.93/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.93/1.57 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 0.93/1.57 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.93/1.57 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.93/1.57 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.93/1.57 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.57 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.93/1.57 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.93/1.57 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.93/1.57 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.93/1.57 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.93/1.57 ) }.
% 0.93/1.57 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.93/1.57 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.93/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.93/1.57 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.93/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.93/1.57 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.93/1.57 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.93/1.57 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.93/1.57 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.93/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.93/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.93/1.57 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.93/1.57 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 0.93/1.57 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 0.93/1.57 tc_Nat_Onat ) ) }.
% 0.93/1.57 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.93/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.93/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.93/1.57 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.93/1.57 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.93/1.57 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.93/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.93/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.93/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.93/1.57 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.93/1.57 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.93/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.93/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.93/1.57 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 0.93/1.57 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 0.93/1.57 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.93/1.57 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.93/1.57 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.93/1.57 c_Polynomial_Odegree( X, Y ) }.
% 0.93/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), ! T =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Y ), T ), hAPP(
% 0.93/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Z ), X ) ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.93/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Y ), T ), hAPP(
% 0.93/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Z ), X ) ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), T =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.93/1.57 { c_Nat_Onat_Onat__size( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.93/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) =
% 0.93/1.57 c_Polynomial_Odegree( X, Z ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.93/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.93/1.57 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.93/1.57 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.93/1.57 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.93/1.57 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.93/1.57 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.57 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.93/1.57 Z ) ), U ), T ) = Y }.
% 0.93/1.57 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.93/1.57 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.57 ( X ), Z ), U ), Y ) }.
% 0.93/1.57 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.57 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.93/1.57 W ) ), U ), Y ) }.
% 0.93/1.57 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.93/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.93/1.57 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.57 ( X ), Z ), U ), Y ) }.
% 0.93/1.57 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.57 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.93/1.57 Z ) ), Y ) ) }.
% 0.93/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.93/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.93/1.57 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.93/1.57 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.93/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.93/1.57 X, Y ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.93/1.57 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.93/1.57 X, Y ) ) }.
% 0.93/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.93/1.57 X, Z, Y ) }.
% 0.93/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.93/1.57 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.93/1.57 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.57 , Y ) ) }.
% 0.93/1.57 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.57 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 0.93/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.93/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.93/1.57 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.93/1.57 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.93/1.57 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ) ) = Z }.
% 0.93/1.57 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.93/1.57 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 0.93/1.57 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.93/1.57 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 0.93/1.57 ), Y ) ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.93/1.57 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 0.93/1.57 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.93/1.57 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.57 }.
% 0.93/1.57 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 0.93/1.57 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.93/1.57 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 0.93/1.57 ) ) }.
% 0.93/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.93/1.57 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.93/1.57 tc_Polynomial_Opoly( X ), Y ) }.
% 0.93/1.57 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.57 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.57 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.93/1.57 c_Polynomial_Odegree( X, Y ) }.
% 0.93/1.57 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.93/1.57 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.93/1.57 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.93/1.57 .
% 0.93/1.57 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.93/1.57 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.93/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.93/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.93/1.57 }.
% 0.93/1.57 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.93/1.57 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.93/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.93/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.93/1.57 }.
% 0.93/1.57 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 0.93/1.57 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.93/1.57 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 0.93/1.57 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 0.93/1.57 c_Polynomial_Odegree( X, Z ) ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 0.93/1.57 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.93/1.57 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.93/1.57 }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 0.93/1.57 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.57 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.93/1.57 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.93/1.57 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 0.93/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.93/1.57 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.93/1.57 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.93/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.93/1.57 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.93/1.57 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ),
% 0.93/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ),
% 0.93/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 0.93/1.57 c_Polynomial_Odegree( X, Y ) ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 0.93/1.57 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.93/1.57 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.93/1.57 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 0.93/1.57 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.93/1.57 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.93/1.57 c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.57 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.93/1.57 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.93/1.57 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.93/1.57 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), skol6( Z, Y ) ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.93/1.57 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = T, T =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y, hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.93/1.57 ), X ), T ) ) }.
% 0.93/1.57 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol6( X, Y ) ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.93/1.57 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = Z, Z =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y, hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.93/1.57 ), X ), Z ) ) }.
% 0.93/1.57 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.93/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( X, X,
% 0.93/1.57 c_Polynomial_Opoly( X, Y ) ), c_Polynomial_Odegree( X, Y ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.93/1.57 c_Polynomial_Odegree( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.93/1.57 , c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( X, X,
% 0.93/1.57 c_Polynomial_Opoly( X, Y ) ) }.
% 0.93/1.57 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_Osize__class_Osize(
% 0.93/1.57 tc_Nat_Onat, X ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.93/1.57 ) ) }.
% 0.93/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.93/1.57 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.93/1.57 { c_Nat_Osize__class_Osize( tc_Nat_Onat, X ) = X }.
% 0.93/1.57 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 0.93/1.57 X, T ) = hAPP( X, U ) }.
% 0.93/1.57 { ! hAPP( X, skol7( X ) ) = hAPP( X, skol22( X ) ),
% 0.93/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 0.93/1.57 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.93/1.57 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.93/1.57 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.93/1.57 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.93/1.57 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.57 }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.93/1.57 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.93/1.57 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.93/1.57 .
% 0.93/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.93/1.57 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.93/1.57 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.93/1.57 .
% 0.93/1.57 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.93/1.57 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.93/1.57 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.93/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.93/1.57 { c_HOL_Obool_Obool__size( c_fTrue ) = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.93/1.57 X ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.93/1.57 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Y ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.93/1.57 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Z ) }.
% 0.93/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.93/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.93/1.57 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, T, Y ) }.
% 0.93/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.93/1.57 , Y, Z ) ) }.
% 0.93/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.93/1.57 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, Z, Y ) }.
% 0.93/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.93/1.57 , T, Y ) ) }.
% 0.93/1.57 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.93/1.57 , Y, T ) ) }.
% 0.93/1.57 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.93/1.57 , T, Y ) ) }.
% 0.93/1.57 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.93/1.57 , T ) ) }.
% 0.93/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.93/1.57 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, Z, Y ) }.
% 0.93/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.93/1.57 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, Z, Y ) }.
% 0.93/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.93/1.57 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.93/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.93/1.57 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.93/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.57 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.93/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.57 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.93/1.57 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.93/1.57 ( X, Y ), Z ) }.
% 0.93/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.93/1.57 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.93/1.57 ( X, Z ), Y ) }.
% 0.93/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.93/1.57 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.93/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ), X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.93/1.57 .
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ), X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.93/1.57 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.93/1.57 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.93/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.93/1.57 .
% 0.93/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.93/1.57 .
% 0.93/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.93/1.57 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.93/1.57 X ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.93/1.57 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.93/1.57 }.
% 0.93/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.93/1.57 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.93/1.57 , X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.93/1.57 .
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.93/1.57 .
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.93/1.57 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.93/1.57 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.93/1.57 .
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.93/1.57 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.93/1.57 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.93/1.57 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.93/1.57 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.93/1.57 ) }.
% 0.93/1.57 { alpha59( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.93/1.57 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.93/1.57 { alpha59( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.93/1.57 ( X, Y ), Z ) ) }.
% 0.93/1.57 { ! alpha59( X, Y, Z ), alpha61( X, Y, Z ), Z = Y }.
% 0.93/1.57 { ! alpha59( X, Y, Z ), alpha61( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.93/1.57 ) ) }.
% 0.93/1.57 { ! alpha61( X, Y, Z ), alpha59( X, Y, Z ) }.
% 0.93/1.57 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha59( X, Y, Z ) }.
% 0.93/1.57 { ! alpha61( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.93/1.57 }.
% 0.93/1.57 { ! alpha61( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.93/1.57 X, Y ), Z ) ), alpha61( X, Y, Z ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.93/1.57 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.93/1.57 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, Y, Z ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.93/1.57 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 0.93/1.57 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 0.93/1.57 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 0.93/1.57 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.93/1.57 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.93/1.57 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.93/1.57 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.57 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.93/1.57 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Polynomial_Opoly( X ), Z, T ), c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Opoly__gcd( X, Y, T ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Polynomial_Opoly( X ), T, Z ), ! c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Polynomial_Opoly( X ), T, Y ), c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z,
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.93/1.57 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 0.93/1.57 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.57 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha7( X, Y, Z, T ),
% 0.93/1.57 alpha31( X, Y, Z, T ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha7( X, Y, Z, T ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha31( X, Y, Z, T ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.57 { ! alpha31( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.57 { ! alpha31( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.57 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha31( X, Y, Z, T ) }.
% 0.93/1.57 { ! alpha7( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.93/1.57 { ! alpha7( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.93/1.57 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha7( X, Y, Z, T ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha8( X, Y, Z, T ),
% 0.93/1.57 alpha32( X, Y, Z, T ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha8( X, Y, Z, T ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha32( X, Y, Z, T ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.57 { ! alpha32( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.57 { ! alpha32( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.57 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha32( X, Y, Z, T ) }.
% 0.93/1.57 { ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.93/1.57 { ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.93/1.57 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha8( X, Y, Z, T ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.57 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.57 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.93/1.57 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.57 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.93/1.57 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.57 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.57 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( X ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.57 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.57 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( X ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.93/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.93/1.57 .
% 0.93/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.93/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.93/1.57 .
% 0.93/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.57 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.57 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.93/1.57 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.57 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.93/1.57 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( X ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.57 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.57 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.93/1.57 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.93/1.57 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.93/1.57 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.93/1.57 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.93/1.57 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.57 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.93/1.57 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.93/1.57 ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.57 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.93/1.57 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.93/1.57 ) ) }.
% 0.93/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.93/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.93/1.57 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.93/1.57 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.93/1.57 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.57 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.93/1.57 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.93/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.57 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.57 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.93/1.57 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( X ) ) }.
% 0.93/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.93/1.57 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.93/1.57 , Z, Y ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.93/1.57 .
% 0.93/1.57 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.93/1.57 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.93/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.57 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.93/1.57 .
% 0.93/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.57 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.93/1.57 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.93/1.57 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.93/1.57 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.93/1.57 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.57 , Y ) }.
% 0.93/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.93/1.57 , Y ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.93/1.57 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.93/1.57 ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.93/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol8( X ) ) }.
% 0.93/1.57 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha9( X, Y ) }.
% 0.93/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.93/1.57 { ! alpha9( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.93/1.57 c_Nat_OSuc( X ) ) }.
% 0.93/1.57 { ! alpha9( X, Y ), Y = c_Nat_OSuc( skol9( Z, Y ) ) }.
% 0.93/1.57 { ! alpha9( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol9( X, Y
% 0.93/1.57 ), X ) }.
% 0.93/1.57 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.93/1.57 ), alpha9( X, Y ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ), Y ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.93/1.57 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Nat_Onat, Y, X ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Nat_Onat, Y, X ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol10( X, Y ) ) ) }.
% 0.93/1.57 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.93/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.93/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.93/1.57 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.93/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.93/1.57 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ), Y ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.93/1.57 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ), Z ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.93/1.57 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.93/1.57 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.93/1.57 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.57 Y ), X ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.57 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.57 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.57 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.57 tc_Nat_Onat ), X ), Y ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.93/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.93/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.93/1.57 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.93/1.57 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.93/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.93/1.57 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.93/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.93/1.57 ), X ) ) }.
% 0.93/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.93/1.57 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.93/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Nat_Onat, Z, X ), Y ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.93/1.57 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.93/1.57 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.93/1.57 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.93/1.57 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.93/1.57 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.93/1.57 ), X ) ) }.
% 0.93/1.57 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.93/1.57 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.93/1.57 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 0.93/1.57 .
% 0.93/1.57 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.93/1.57 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.93/1.57 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.93/1.57 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.93/1.57 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.93/1.57 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.93/1.57 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 0.93/1.57 }.
% 0.93/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.57 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.93/1.57 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.93/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.93/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.57 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.93/1.57 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.57 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.93/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.57 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.93/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.93/1.57 ( X, Z, W ) ), U ), Y ) ) }.
% 0.93/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.93/1.57 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.93/1.57 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.57 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.93/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.57 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.93/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.93/1.57 X, W, Z ) ), U ), T ), Y ) }.
% 0.93/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.57 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.93/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.57 ( X ), Z ), U ), Y ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.93/1.57 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.93/1.57 ) ) = X }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.93/1.57 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.93/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.93/1.57 , ! alpha10( X, Y, Z ) }.
% 0.93/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.93/1.57 , ! alpha33( X, Y, Z ) }.
% 0.93/1.57 { alpha10( X, Y, Z ), alpha33( X, Y, Z ), hBOOL( hAPP( Z,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.93/1.57 { ! alpha33( X, Y, Z ), ! hBOOL( hAPP( Z, skol11( T, U, Z ) ) ) }.
% 0.93/1.57 { ! alpha33( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.93/1.57 skol11( X, Y, Z ) ) }.
% 0.93/1.57 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.93/1.57 ) ), alpha33( X, Y, Z ) }.
% 0.93/1.57 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.93/1.57 }.
% 0.93/1.57 { ! alpha10( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ) ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha10( X, Y, Z ) }.
% 0.93/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.93/1.57 , alpha11( X, Y, Z ) }.
% 0.93/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.93/1.57 , alpha34( X, Y, Z ) }.
% 0.93/1.57 { ! alpha11( X, Y, Z ), ! alpha34( X, Y, Z ), hBOOL( hAPP( Z,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.93/1.57 { ! alpha34( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.93/1.57 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.93/1.57 { ! hBOOL( hAPP( Z, skol12( T, U, Z ) ) ), alpha34( X, Y, Z ) }.
% 0.93/1.57 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol12( X, Y, Z ) ),
% 0.93/1.57 alpha34( X, Y, Z ) }.
% 0.93/1.57 { ! alpha11( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.93/1.57 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.93/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha11( X, Y, Z ) }
% 0.93/1.57 .
% 0.93/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha11
% 0.93/1.57 ( X, Y, Z ) }.
% 0.93/1.57 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.57 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 0.93/1.57 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.93/1.57 c_Groups_Oone__class_Oone( X ) ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.93/1.57 ( X ), Y ), Z ) ) }.
% 0.93/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.93/1.57 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.93/1.57 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.93/1.57 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.93/1.57 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.93/1.57 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 0.93/1.57 { c_HOL_Obool_Obool__size( c_fFalse ) = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.93/1.57 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ), Y ) }.
% 0.93/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.93/1.57 ), X ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Polynomial_Opoly( X ), Z, Y ), alpha62( X, Y, Z, T ), ! Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.93/1.57 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Polynomial_Opoly( X ), Z, Y ), alpha62( X, Y, Z, T ), ! hAPP(
% 0.93/1.57 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.93/1.57 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 0.93/1.57 .
% 0.93/1.57 { ! alpha62( X, Y, Z, T ), alpha63( X, Y, Z, T ), alpha60( X, Y, T ) }.
% 0.93/1.57 { ! alpha62( X, Y, Z, T ), alpha63( X, Y, Z, T ), ! hAPP(
% 0.93/1.57 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { ! alpha63( X, Y, Z, T ), alpha62( X, Y, Z, T ) }.
% 0.93/1.57 { ! alpha60( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.93/1.57 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.57 alpha62( X, Y, Z, T ) }.
% 0.93/1.57 { ! alpha63( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.93/1.57 ( X ), Z, T ), alpha64( X, Y, Z, T ) }.
% 0.93/1.57 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, T ), alpha63( X, Y
% 0.93/1.57 , Z, T ) }.
% 0.93/1.57 { ! alpha64( X, Y, Z, T ), alpha63( X, Y, Z, T ) }.
% 0.93/1.57 { ! alpha64( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.93/1.57 ), skol13( X, Y, U, W ), Y ) }.
% 0.93/1.57 { ! alpha64( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.93/1.57 ), skol13( X, Y, U, T ), T ) }.
% 0.93/1.57 { ! alpha64( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.93/1.57 ( X ), skol13( X, Y, Z, T ), Z ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Y ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, T ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Z ), alpha64( X, Y
% 0.93/1.57 , Z, T ) }.
% 0.93/1.57 { ! alpha60( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.57 { ! alpha60( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha60( X, Y, Z
% 0.93/1.57 ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.93/1.57 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 0.93/1.57 }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.93/1.57 , alpha49( X, Y, Z, T ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha49( X, Y, Z, T ),
% 0.93/1.57 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 0.93/1.57 { ! alpha49( X, Y, Z, T ), alpha12( X, Z, T ) }.
% 0.93/1.57 { ! alpha49( X, Y, Z, T ), alpha35( X, Y, T ) }.
% 0.93/1.57 { ! alpha12( X, Z, T ), ! alpha35( X, Y, T ), alpha49( X, Y, Z, T ) }.
% 0.93/1.57 { ! alpha35( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), alpha50( X, Y, Z ) }.
% 0.93/1.57 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha35( X
% 0.93/1.57 , Y, Z ) }.
% 0.93/1.57 { ! alpha50( X, Y, Z ), alpha35( X, Y, Z ) }.
% 0.93/1.57 { ! alpha50( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.57 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 0.93/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha50( X
% 0.93/1.57 , Y, Z ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 0.93/1.57 ), c_Polynomial_Odegree( X, Z ) ), alpha50( X, Y, Z ) }.
% 0.93/1.57 { ! alpha12( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.57 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha12( X,
% 0.93/1.57 Y, Z ) }.
% 0.93/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha12( X
% 0.93/1.57 , Y, Z ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.93/1.57 .
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.93/1.57 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.93/1.57 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.93/1.57 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.93/1.57 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 0.93/1.57 .
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.93/1.57 , c_Polynomial_Opdivmod__rel( X, c_Polynomial_Osmult( X, W, U ), T,
% 0.93/1.57 c_Polynomial_Osmult( X, W, Z ), c_Polynomial_Osmult( X, W, Y ) ) }.
% 0.93/1.57 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.93/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.93/1.57 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.93/1.57 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.93/1.57 = X }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.93/1.57 tc_Int_Oint ) ) ) }.
% 0.93/1.57 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.93/1.57 tc_Int_Oint ) ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.93/1.57 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.93/1.57 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.93/1.57 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.57 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.57 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.93/1.57 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.93/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.93/1.57 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 0.93/1.57 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 0.93/1.57 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 0.93/1.57 ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.93/1.57 , T = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! V0 =
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 0.93/1.57 c_Polynomial_OpCons( X, W, Y ) ), c_Polynomial_Odegree( X, T ) ), hAPP(
% 0.93/1.57 c_Polynomial_Ocoeff( X, T ), c_Polynomial_Odegree( X, T ) ) ),
% 0.93/1.57 c_Polynomial_Opdivmod__rel( X, c_Polynomial_OpCons( X, W, U ), T,
% 0.93/1.57 c_Polynomial_OpCons( X, V0, Z ), c_Groups_Ominus__class_Ominus(
% 0.93/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, W, Y ),
% 0.93/1.57 c_Polynomial_Osmult( X, V0, T ) ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.93/1.57 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.93/1.57 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 0.93/1.57 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.93/1.57 { ! class_RealVector_Oreal__normed__field( X ),
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 0.93/1.57 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 0.93/1.57 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.93/1.57 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.93/1.57 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.93/1.57 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.93/1.57 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.93/1.57 { ! class_RealVector_Oreal__normed__field( X ),
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.93/1.57 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.93/1.57 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 0.93/1.57 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.93/1.57 { ! class_RealVector_Oreal__normed__field( X ),
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.93/1.57 ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.93/1.57 { ! class_Rings_Odivision__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.93/1.57 ), Y ) }.
% 0.93/1.57 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 0.93/1.57 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.93/1.57 { ! class_RealVector_Oreal__normed__field( X ),
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.93/1.57 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.57 }.
% 0.93/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.57 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.57 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.93/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.57 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.93/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.57 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.93/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.57 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.93/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.57 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.93/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.57 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.93/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.93/1.57 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.93/1.57 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.57 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 0.93/1.57 ( X ) }.
% 0.93/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.57 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.93/1.57 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 0.93/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.57 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.93/1.57 c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.57 , c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.57 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.93/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.57 , c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X
% 0.93/1.57 , Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.93/1.57 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 0.93/1.57 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 0.93/1.57 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.57 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 0.93/1.57 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 0.93/1.57 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.57 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.93/1.57 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.57 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.93/1.57 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.57 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.93/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 0.93/1.57 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.93/1.57 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.93/1.57 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.93/1.57 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha13( X, Y, Z ), alpha36
% 0.93/1.57 ( X, Y, Z ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha13( X, Y, Z
% 0.93/1.57 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha36( X, Y, Z
% 0.93/1.57 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.93/1.57 { ! alpha36( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.57 { ! alpha36( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.57 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.57 ), alpha36( X, Y, Z ) }.
% 0.93/1.57 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.93/1.57 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.93/1.57 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.57 ), alpha13( X, Y, Z ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 0.93/1.57 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha14( X, Y, Z ), alpha37( X,
% 0.93/1.57 Y, Z ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha14( X, Y, Z
% 0.93/1.57 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.93/1.57 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha37( X, Y, Z
% 0.93/1.57 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.93/1.57 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.57 { ! alpha37( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.57 { ! alpha37( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.57 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.57 ), alpha37( X, Y, Z ) }.
% 0.93/1.57 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.93/1.57 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.93/1.57 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.57 ), alpha14( X, Y, Z ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.93/1.57 , Y, Z ) ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.93/1.57 , Y, Z ) ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha38( X, Y, Z, T ) }.
% 0.93/1.57 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha15( X, Y, T ) }.
% 0.93/1.57 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha38( X, Y, Z, T ), !
% 0.93/1.57 alpha15( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.93/1.57 { ! alpha38( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 0.93/1.57 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.93/1.57 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha38( X, Y, Z, T ) }.
% 0.93/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha38(
% 0.93/1.57 X, Y, Z, T ) }.
% 0.93/1.57 { ! alpha15( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { Y = c_Groups_Ozero__class_Ozero( X ), alpha15( X, Y, Z ) }.
% 0.93/1.57 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha15( X, Y, Z ) }.
% 0.93/1.57 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha39( X, Y, Z, T ) }.
% 0.93/1.57 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha16( X, Y, Z ) }.
% 0.93/1.57 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha39( X, Y, Z, T ), !
% 0.93/1.57 alpha16( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 0.93/1.57 { ! alpha39( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 0.93/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.93/1.57 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha39( X, Y, Z, T ) }.
% 0.93/1.57 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha39(
% 0.93/1.57 X, Y, Z, T ) }.
% 0.93/1.57 { ! alpha16( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.57 { Z = c_Groups_Ozero__class_Ozero( X ), alpha16( X, Y, Z ) }.
% 0.93/1.57 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha16( X, Y, Z ) }.
% 0.93/1.57 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.93/1.57 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 0.93/1.57 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.57 Z, Y ) ), alpha40( X, Y, Z, T ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.57 Z, Y ) ), alpha51( X, Y, Z, T ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha40( X, Y, Z
% 0.93/1.57 , T ), ! alpha51( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.93/1.57 { ! alpha51( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), Y ), alpha54( X, Y, Z, T ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.93/1.57 , alpha51( X, Y, Z, T ) }.
% 0.93/1.57 { ! alpha54( X, Y, Z, T ), alpha51( X, Y, Z, T ) }.
% 0.93/1.57 { ! alpha54( X, Y, Z, T ), alpha57( X, Y, Z, T ) }.
% 0.93/1.57 { ! alpha54( X, Y, Z, T ), alpha17( X, Y, T ) }.
% 0.93/1.57 { ! alpha57( X, Y, Z, T ), ! alpha17( X, Y, T ), alpha54( X, Y, Z, T ) }.
% 0.93/1.57 { ! alpha57( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.57 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.57 alpha57( X, Y, Z, T ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha57( X, Y, Z, T ) }.
% 0.93/1.57 { ! alpha40( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.93/1.57 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.57 alpha40( X, Y, Z, T ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha40( X, Y, Z, T )
% 0.93/1.57 }.
% 0.93/1.57 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.57 , alpha17( X, Y, Z ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.57 , alpha17( X, Y, Z ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.93/1.57 Z ), Y ), alpha41( X, Y, Z, T ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.93/1.57 Z ), Y ), alpha52( X, Y, Z, T ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha41( X, Y, Z
% 0.93/1.57 , T ), ! alpha52( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.93/1.57 { ! alpha52( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), Z ), alpha55( X, Y, Z, T ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.93/1.57 , alpha52( X, Y, Z, T ) }.
% 0.93/1.57 { ! alpha55( X, Y, Z, T ), alpha52( X, Y, Z, T ) }.
% 0.93/1.57 { ! alpha55( X, Y, Z, T ), alpha58( X, Y, Z, T ) }.
% 0.93/1.57 { ! alpha55( X, Y, Z, T ), alpha18( X, Y, Z ) }.
% 0.93/1.57 { ! alpha58( X, Y, Z, T ), ! alpha18( X, Y, Z ), alpha55( X, Y, Z, T ) }.
% 0.93/1.57 { ! alpha58( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.93/1.57 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.57 alpha58( X, Y, Z, T ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha58( X, Y, Z, T )
% 0.93/1.57 }.
% 0.93/1.57 { ! alpha41( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.57 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.93/1.57 alpha41( X, Y, Z, T ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha41( X, Y, Z, T ) }.
% 0.93/1.57 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.57 , alpha18( X, Y, Z ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.93/1.57 , alpha18( X, Y, Z ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.57 Z, Y ) ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.93/1.57 Y ), Z ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.93/1.57 Y ), Z ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.57 Z, Y ) ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.57 Z, Y ) ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.93/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.93/1.57 Y ), Z ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.57 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.93/1.57 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.93/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.93/1.57 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.93/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 0.93/1.57 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.93/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 0.93/1.57 .
% 0.93/1.57 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.93/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 0.93/1.57 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.93/1.57 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 0.93/1.57 .
% 0.93/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.93/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.57 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.93/1.57 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 0.93/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T, Z ), Y ) =
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.93/1.57 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 0.93/1.57 tc_Polynomial_Opoly( X ), Z, Y ) ), c_Polynomial_Osmult( X,
% 0.93/1.57 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 0.93/1.57 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 0.93/1.57 tc_Polynomial_Opoly( X ), Z, Y ) ) ), c_Polynomial_Odegree( X, Y ) ),
% 0.93/1.57 hAPP( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y )
% 0.93/1.57 ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.93/1.57 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.57 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.93/1.57 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.93/1.57 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.93/1.57 alpha19( X, Y, Z ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.93/1.57 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__idom( X ), ! alpha19( X, Y, Z ),
% 0.93/1.57 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.93/1.57 { ! alpha19( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.57 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.93/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.93/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.93/1.57 alpha19( X, Y, Z ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T,
% 0.93/1.57 c_Polynomial_Osmult( X, Y, Z ) ) = c_Divides_Odiv__class_Omod(
% 0.93/1.57 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.93/1.57 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.93/1.57 , c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.93/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 0.93/1.57 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Omod(
% 0.93/1.57 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.93/1.57 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.93/1.57 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.93/1.57 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.93/1.57 ( X ), Z, Y ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.93/1.57 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.93/1.57 tc_Polynomial_Opoly( X ), Y ) ) = c_Divides_Odiv__class_Omod(
% 0.93/1.57 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.93/1.57 c_Polynomial_Opoly__gcd( X, Y, c_Divides_Odiv__class_Omod(
% 0.93/1.57 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.93/1.57 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.93/1.57 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.93/1.57 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.93/1.57 .
% 0.93/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.57 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.93/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 0.93/1.57 tc_Polynomial_Opoly( X ), Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.57 c_Polynomial_Odegree( X, c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.93/1.57 ( X ), Z, Y ) ), c_Polynomial_Odegree( X, Y ) ) }.
% 0.93/1.57 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.93/1.57 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.93/1.57 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.93/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.93/1.57 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 X ) }.
% 0.93/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 0.93/1.57 Z ) = c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.93/1.57 ) }.
% 0.93/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.93/1.57 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 0.93/1.57 X ) }.
% 0.93/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.93/1.57 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 0.93/1.57 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.93/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) ), Y ) =
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.93/1.57 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) =
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), c_Rings_Odvd__class_Odvd
% 0.93/1.57 ( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, X ) ) }
% 0.93/1.57 .
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus
% 0.93/1.57 ( tc_Int_Oint, Z, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y )
% 0.93/1.57 = c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) }.
% 0.93/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.93/1.57 tc_Int_Oint, Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.93/1.57 tc_Int_Oint, Z, Y ), X ) }.
% 0.93/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.93/1.57 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ), X ), Y ) =
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.93/1.57 tc_Int_Oint, Z, X ), Y ) }.
% 0.93/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 0.93/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.93/1.57 { ! c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.93/1.57 c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 0.93/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol14( X, Y ) ) }.
% 0.93/1.57 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 0.93/1.57 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.57 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol15( X, Y ) ) }.
% 0.93/1.57 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 0.93/1.57 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.93/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 0.93/1.57 ), Y ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 0.93/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.93/1.57 ( tc_Int_Oint, Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.93/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 0.93/1.57 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Divides_Odiv__class_Omod(
% 0.93/1.57 tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X ),
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.93/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.93/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.93/1.57 tc_Int_Oint, Y, c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) }.
% 0.93/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 0.93/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.93/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.93/1.57 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.93/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.93/1.57 ( tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.93/1.57 ( tc_Int_Oint, Y ), X ) }.
% 0.93/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.93/1.57 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.93/1.57 ( tc_Int_Oint, Y, X ) ) }.
% 0.93/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.93/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.93/1.57 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) ) }
% 0.93/1.57 .
% 0.93/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.93/1.57 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 0.93/1.57 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 0.93/1.57 }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.57 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.93/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.93/1.57 ( tc_Int_Oint, Y, X ) ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.93/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.93/1.57 tc_Nat_Onat, Y, X ), X ) }.
% 0.93/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.93/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.93/1.57 tc_Nat_Onat, Y, X ), X ) }.
% 0.93/1.57 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.93/1.57 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.93/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.93/1.57 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.93/1.57 tc_Int_Oint, Y, X ), X ) }.
% 0.93/1.57 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.93/1.57 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.93/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.93/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.93/1.57 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.93/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.93/1.57 ( tc_Int_Oint, Y, X ) ) }.
% 0.93/1.57 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.93/1.57 alpha20( X, Y, Z ) }.
% 0.93/1.57 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.93/1.57 alpha42( X, Y, Z ) }.
% 0.93/1.57 { ! alpha20( X, Y, Z ), ! alpha42( X, Y, Z ), hBOOL( hAPP( Z,
% 0.93/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ) }.
% 0.93/1.57 { ! alpha42( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.57 alpha53( X, Y, Z ) }.
% 0.93/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha42( X, Y, Z ) }.
% 0.93/1.57 { ! alpha53( X, Y, Z ), alpha42( X, Y, Z ) }.
% 0.93/1.57 { ! alpha53( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.93/1.57 ), alpha56( X, Y, Z, T ) }.
% 0.93/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol16( X, T, U ), X ),
% 0.93/1.57 alpha53( X, Y, Z ) }.
% 0.93/1.57 { ! alpha56( X, Y, Z, skol16( X, Y, Z ) ), alpha53( X, Y, Z ) }.
% 0.93/1.57 { ! alpha56( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.93/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.93/1.57 hBOOL( hAPP( Z, T ) ) }.
% 0.93/1.57 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol17( X, Y, T ) ), T
% 0.93/1.57 ), alpha56( X, Y, Z, T ) }.
% 0.93/1.57 { ! hBOOL( hAPP( Z, T ) ), alpha56( X, Y, Z, T ) }.
% 0.93/1.57 { ! alpha20( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.57 hBOOL( hAPP( Z, Y ) ) }.
% 0.93/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha20( X, Y, Z ) }.
% 0.93/1.57 { ! hBOOL( hAPP( Z, Y ) ), alpha20( X, Y, Z ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.93/1.58 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.93/1.58 c_Divides_Odiv__class_Omod( tc_Nat_Onat, T, X ) ), Z ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.93/1.58 tc_Nat_Onat ), X ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X )
% 0.93/1.58 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.93/1.58 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 0.93/1.58 X, Z, Y ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.93/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.93/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.93/1.58 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.58 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.93/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.93/1.58 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.58 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.93/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.93/1.58 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.58 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 0.93/1.58 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.93/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 0.93/1.58 , Y ) ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.93/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.93/1.58 ), Z ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.93/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 0.93/1.58 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.93/1.58 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.93/1.58 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.93/1.58 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.58 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.93/1.58 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 0.93/1.58 ( X, Z, Y ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.93/1.58 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.93/1.58 ( X, Y, Z ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.93/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.93/1.58 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 0.93/1.58 , Y ) ), Y ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.93/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.93/1.58 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.93/1.58 ), Z ), Y ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.93/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.93/1.58 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.93/1.58 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.93/1.58 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.93/1.58 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.93/1.58 T, Z ), Y ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.93/1.58 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 0.93/1.58 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.93/1.58 T, Y ), Z ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.93/1.58 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.93/1.58 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.93/1.58 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 0.93/1.58 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 0.93/1.58 ), Z ) }.
% 0.93/1.58 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.93/1.58 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 0.93/1.58 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.93/1.58 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 0.93/1.58 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 0.93/1.58 , U ), Z ) }.
% 0.93/1.58 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.93/1.58 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.93/1.58 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.93/1.58 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 0.93/1.58 Y ) ), Y ) }.
% 0.93/1.58 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.93/1.58 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.93/1.58 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.93/1.58 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 0.93/1.58 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.93/1.58 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.93/1.58 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.93/1.58 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.93/1.58 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.93/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.93/1.58 ( X, c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Omod( X, Z
% 0.93/1.58 , Y ) ), Y ) }.
% 0.93/1.58 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.93/1.58 = c_Divides_Odiv__class_Omod( X, Y, Z ), c_Divides_Odiv__class_Omod( X,
% 0.93/1.58 c_Groups_Ouminus__class_Ouminus( X, T ), Z ) = c_Divides_Odiv__class_Omod
% 0.93/1.58 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.93/1.58 ), ! c_Rings_Odvd__class_Odvd( X, Z, c_Divides_Odiv__class_Omod( X, T, Y
% 0.93/1.58 ) ), c_Rings_Odvd__class_Odvd( X, Z, T ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.93/1.58 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 0.93/1.58 , c_Divides_Odiv__class_Omod( X, T, Y ) ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.93/1.58 ), c_Divides_Odiv__class_Omod( X, c_Divides_Odiv__class_Omod( X, T, Y )
% 0.93/1.58 , Z ) = c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.93/1.58 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 0.93/1.58 , c_Divides_Odiv__class_Omod( X, Y, T ) ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, T,
% 0.93/1.58 c_Divides_Odiv__class_Omod( X, Z, Y ) ), ! c_Rings_Odvd__class_Odvd( X, T
% 0.93/1.58 , Y ), c_Rings_Odvd__class_Odvd( X, T, Z ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.93/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.93/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.93/1.58 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.93/1.58 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.93/1.58 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.58 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 0.93/1.58 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 0.93/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 0.93/1.58 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.58 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.93/1.58 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 0.93/1.58 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.93/1.58 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.93/1.58 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 0.93/1.58 ( X ) ) ) }.
% 0.93/1.58 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 0.93/1.58 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 0.93/1.58 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 0.93/1.58 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 0.93/1.58 c_Polynomial_Opoly__gcd( X, Z, c_Divides_Odiv__class_Omod(
% 0.93/1.58 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.93/1.58 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.93/1.58 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, Y ) ), Y ),
% 0.93/1.58 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) ), X ) =
% 0.93/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) }.
% 0.93/1.58 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.93/1.58 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.93/1.58 ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 0.93/1.58 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ), X ) =
% 0.93/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) }.
% 0.93/1.58 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.93/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.93/1.58 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.93/1.58 { Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.93/1.58 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 0.93/1.58 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.93/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 0.93/1.58 ( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.93/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) =
% 0.93/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.93/1.58 ( tc_Int_Oint, X, Y ) ) }.
% 0.93/1.58 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.93/1.58 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.93/1.58 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.93/1.58 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.93/1.58 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.93/1.58 tc_Int_Oint ) ) = X }.
% 0.93/1.58 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.93/1.58 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.93/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.93/1.58 tc_Int_Oint, Z, X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.93/1.58 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, X ),
% 0.93/1.58 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.93/1.58 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.93/1.58 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.93/1.58 tc_Int_Oint ), Y ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.93/1.58 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.93/1.58 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.93/1.58 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.93/1.58 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.93/1.58 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.93/1.58 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.93/1.58 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y,
% 0.93/1.58 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.93/1.58 ( tc_Int_Oint, Y ), X ) }.
% 0.93/1.58 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.93/1.58 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.93/1.58 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.93/1.58 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.93/1.58 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.93/1.58 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 0.93/1.58 , c_Divides_Odiv__class_Odiv( X, Y, Z ), c_Divides_Odiv__class_Odiv( X, T
% 0.93/1.58 , Z ) ), c_Rings_Odvd__class_Odvd( X, Y, T ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.93/1.58 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 0.93/1.58 , Y, T ), c_Rings_Odvd__class_Odvd( X, c_Divides_Odiv__class_Odiv( X, Y,
% 0.93/1.58 Z ), c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.93/1.58 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 0.93/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.93/1.58 ), ! c_Rings_Odvd__class_Odvd( X, U, T ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.93/1.58 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 0.93/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.93/1.58 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.93/1.58 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.93/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.93/1.58 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), Z ) = Y }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.93/1.58 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = c_Divides_Odiv__class_Odiv( X,
% 0.93/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.93/1.58 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = Y }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.93/1.58 }.
% 0.93/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 0.93/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.93/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.93/1.58 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.93/1.58 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.93/1.58 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.58 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.93/1.58 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.93/1.58 , Y ) ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.58 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.93/1.58 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.93/1.58 .
% 0.93/1.58 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.58 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.93/1.58 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( X ) ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.58 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.58 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.58 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.93/1.58 .
% 0.93/1.58 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.58 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.58 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.93/1.58 { ! class_Fields_Ofield( X ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.93/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.93/1.58 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.58 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Y, Z ) }.
% 0.93/1.58 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 0.93/1.58 , Y = c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.58 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 0.93/1.58 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 0.93/1.58 = c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.58 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.58 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.93/1.58 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.93/1.58 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Z
% 0.93/1.58 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.93/1.58 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.93/1.58 Y ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X )
% 0.93/1.58 , Y ) }.
% 0.93/1.58 { ! class_Fields_Ofield( X ), c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.93/1.58 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) }
% 0.93/1.58 .
% 0.93/1.58 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.93/1.58 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.58 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.58 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.93/1.58 }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.93/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.93/1.58 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.93/1.58 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.93/1.58 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.93/1.58 c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.58 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.93/1.58 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.93/1.58 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.93/1.58 .
% 0.93/1.58 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.58 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.93/1.58 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.93/1.58 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.58 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 0.93/1.58 ) ), Y ) }.
% 0.93/1.58 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.93/1.58 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.93/1.58 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.93/1.58 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.93/1.58 .
% 0.93/1.58 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 0.93/1.58 , Y ) ) = Y }.
% 0.93/1.58 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.93/1.58 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.58 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.58 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.93/1.58 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.58 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.93/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.58 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.58 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 0.93/1.58 X, Y ) ) = Y }.
% 0.93/1.58 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.93/1.58 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( X ) }.
% 0.93/1.58 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.93/1.58 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 0.93/1.58 = Y }.
% 0.93/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.93/1.58 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.58 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.58 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.93/1.58 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.93/1.58 ) }.
% 0.93/1.58 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.93/1.58 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.58 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 }.
% 0.93/1.58 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.93/1.58 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.93/1.58 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.93/1.58 ) ), Z ) }.
% 0.93/1.58 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 0.93/1.58 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 0.93/1.58 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.58 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.93/1.58 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 0.93/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 0.93/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.93/1.58 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Divides_Odiv__class_Odiv( X
% 0.93/1.58 , c_Groups_Oplus__class_Oplus( X, Y, T ), Z ) =
% 0.93/1.58 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Y, Z ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.93/1.58 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( X ) }.
% 0.93/1.58 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( X, Y, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.93/1.58 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 0.93/1.58 , Z ) ) }.
% 0.93/1.58 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z
% 0.93/1.58 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 0.93/1.58 , Z ) ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.93/1.58 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.93/1.58 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.93/1.58 ( c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.58 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.93/1.58 .
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.58 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.93/1.58 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.93/1.58 .
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.58 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.93/1.58 .
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.58 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.93/1.58 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.93/1.58 .
% 0.93/1.58 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.93/1.58 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.93/1.58 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.93/1.58 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.93/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.93/1.58 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.58 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.58 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.58 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 0.93/1.58 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.93/1.58 ) ) }.
% 0.93/1.58 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 0.93/1.58 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.93/1.58 Y ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.93/1.58 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.93/1.58 c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.58 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 0.93/1.58 ) }.
% 0.93/1.58 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.93/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.93/1.58 c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.58 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.93/1.58 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) }
% 0.93/1.58 .
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.93/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 0.93/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.93/1.58 tc_Int_Oint, X, Y ), X ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 0.93/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.93/1.58 tc_Int_Oint, Z, Y ), X ) }.
% 0.93/1.58 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.93/1.58 c_Polynomial_Opdivmod__rel( X, W, U, T, Z ), c_Polynomial_Opdivmod__rel(
% 0.93/1.58 X, W, c_Polynomial_Osmult( X, Y, U ), c_Polynomial_Osmult( X,
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ), T ), Z ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.93/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 0.93/1.58 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.93/1.58 ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.93/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.93/1.58 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.93/1.58 ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 0.93/1.58 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.93/1.58 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 0.93/1.58 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.93/1.58 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 0.93/1.58 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), !
% 0.93/1.58 c_Divides_Odiv__class_Odiv( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U
% 0.93/1.58 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP(
% 0.93/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 0.93/1.58 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), ! hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 0.93/1.58 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! c_Divides_Odiv__class_Odiv( X
% 0.93/1.58 , Z, Y ) = T, Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y
% 0.93/1.58 ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! Z = hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), c_Divides_Odiv__class_Odiv
% 0.93/1.58 ( X, Z, Y ) = T }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.58 c_Divides_Odiv__class_Omod( X, Z, Y ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 0.93/1.58 ), Y ) ) = Z }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.93/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), c_Divides_Odiv__class_Omod( X, Y
% 0.93/1.58 , Z ) ) = Y }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.93/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X
% 0.93/1.58 , Z, Y ) ), Y ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.58 ( X ), T ), c_Divides_Odiv__class_Odiv( X, Z, T ) ),
% 0.93/1.58 c_Divides_Odiv__class_Omod( X, Z, T ) ), Y ) =
% 0.93/1.58 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.93/1.58 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.58 ( X ), c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ),
% 0.93/1.58 c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ) =
% 0.93/1.58 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.93/1.58 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.58 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.93/1.58 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.58 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.93/1.58 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.58 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 0.93/1.58 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 0.93/1.58 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.93/1.58 Y ) ), c_Groups_Ominus__class_Ominus( X, Y, Z ) ) ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, hAPP(
% 0.93/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.93/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.93/1.58 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.93/1.58 tc_Int_Oint, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y
% 0.93/1.58 ) ) }.
% 0.93/1.58 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.93/1.58 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.93/1.58 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.93/1.58 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.93/1.58 ( tc_Int_Oint, Y, X ) ) }.
% 0.93/1.58 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.93/1.58 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.93/1.58 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.93/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.93/1.58 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.93/1.58 ( tc_Int_Oint, Y, X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.93/1.58 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.93/1.58 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.93/1.58 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.93/1.58 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.93/1.58 ( tc_Int_Oint, Y, X ) ) }.
% 0.93/1.58 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.93/1.58 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.93/1.58 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.93/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.93/1.58 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.93/1.58 ( tc_Int_Oint, Y, X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.93/1.58 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.58 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ), T ) =
% 0.93/1.58 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.93/1.58 Y ) ), c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus
% 0.93/1.58 ( X, Y, Z ), T ) ) ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.58 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.93/1.58 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.93/1.58 }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.93/1.58 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.93/1.58 .
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.58 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.93/1.58 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.93/1.58 }.
% 0.93/1.58 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.58 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.58 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.58 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.58 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.58 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.58 c_Groups_Oone__class_Oone( X ) ) }.
% 0.93/1.58 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.93/1.58 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 0.93/1.58 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.93/1.58 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha21( X, Y, T,
% 0.93/1.58 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha21( X, Y, skol18( X, Y
% 0.93/1.58 , Z ), skol23( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.93/1.58 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.93/1.58 skol18( X, Y, Z ) ), skol23( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.93/1.58 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.93/1.58 { ! alpha21( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T
% 0.93/1.58 ) }.
% 0.93/1.58 { ! alpha21( X, Y, Z, T ), alpha43( X, Y, Z, T ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha43( X, Y, Z
% 0.93/1.58 , T ), alpha21( X, Y, Z, T ) }.
% 0.93/1.58 { ! alpha43( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.58 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.93/1.58 { ! alpha43( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.93/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.93/1.58 .
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.93/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha43( X,
% 0.93/1.58 Y, Z, T ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv
% 0.93/1.58 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X )
% 0.93/1.58 ) ), ! alpha22( X, Y, T, U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( tc_Int_Oint ), X ), alpha22( X, Y, skol19( X, Y, Z ), skol24( X, Y, Z )
% 0.93/1.58 ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X )
% 0.93/1.58 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, skol19( X, Y, Z ) ), skol24
% 0.93/1.58 ( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.93/1.58 tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 0.93/1.58 ) }.
% 0.93/1.58 { ! alpha22( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ) }.
% 0.93/1.58 { ! alpha22( X, Y, Z, T ), alpha44( X, Y, Z, T ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha44( X, Y, Z, T )
% 0.93/1.58 , alpha22( X, Y, Z, T ) }.
% 0.93/1.58 { ! alpha44( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.93/1.58 ) }.
% 0.93/1.58 { ! alpha44( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.93/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.93/1.58 .
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.93/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha44( X,
% 0.93/1.58 Y, Z, T ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.93/1.58 tc_Int_Oint, X, Y ) ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.58 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 0.93/1.58 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.58 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.93/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.93/1.58 tc_Nat_Onat, Z, X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.58 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, X ),
% 0.93/1.58 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.93/1.58 tc_Int_Oint, X, Y ) ) }.
% 0.93/1.58 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 0.93/1.58 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.93/1.58 tc_Nat_Onat, Z, Y ), X ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.58 ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.93/1.58 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.93/1.58 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.93/1.58 ) ) }.
% 0.93/1.58 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.58 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.93/1.58 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.93/1.58 , c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 0.93/1.58 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.93/1.58 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.93/1.58 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.93/1.58 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.93/1.58 ( X ), Z, Y ) ) }.
% 0.93/1.58 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.93/1.58 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.93/1.58 tc_Polynomial_Opoly( X ), Y ) ) = c_Groups_Ouminus__class_Ouminus(
% 0.93/1.58 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.93/1.58 ( X ), Z, Y ) ) }.
% 0.93/1.58 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.93/1.58 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 0.93/1.58 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Odiv(
% 0.93/1.58 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.93/1.58 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.93/1.58 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 0.93/1.58 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.93/1.58 ( X ), T, Z ), Y ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.93/1.58 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 0.93/1.58 ( tc_Int_Oint, Y, X ), X = Y }.
% 0.93/1.58 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Z, Y,
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ),
% 0.93/1.58 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.93/1.58 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha23( X, Y
% 0.93/1.58 , Z ), alpha45( X, Y, Z ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha23( X, Y, Z ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha45( X, Y, Z ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.58 { ! alpha45( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.58 { ! alpha45( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.93/1.58 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ), alpha45( X, Y, Z ) }.
% 0.93/1.58 { ! alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.93/1.58 { ! alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), Y ), alpha23( X, Y, Z ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( X ) ), alpha24( X, Y, Z ), alpha46( X, Y, Z ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha24( X, Y, Z ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( X ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha46( X, Y, Z ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( X ) ) }.
% 0.93/1.58 { ! alpha46( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.58 { ! alpha46( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.93/1.58 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( X ), Y ), alpha46( X, Y, Z ) }.
% 0.93/1.58 { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.93/1.58 { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ), alpha24( X, Y, Z ) }.
% 0.93/1.58 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.58 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.58 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.58 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.58 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.58 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( X ) ) }.
% 0.93/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.58 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.93/1.58 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.58 { ! class_Rings_Oordered__semiring( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.93/1.58 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.93/1.58 { ! class_Rings_Oordered__semiring( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.93/1.58 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.58 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.93/1.58 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.58 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.93/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.58 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.93/1.58 { ! class_Rings_Oordered__semiring( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.93/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.58 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.93/1.58 { ! class_Rings_Oordered__semiring( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.58 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.93/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.58 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.93/1.58 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.58 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.93/1.58 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.58 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.93/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.58 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.58 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( X ) ) }.
% 0.93/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.58 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.58 ) }.
% 0.93/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.93/1.58 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.93/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.93/1.58 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 ) }.
% 0.93/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.93/1.58 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.58 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.93/1.58 ) }.
% 0.93/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.58 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.93/1.58 .
% 0.93/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.58 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.93/1.58 .
% 0.93/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.58 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.93/1.58 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.93/1.58 Y, Z ) ) }.
% 0.93/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.93/1.58 Z, Y ) ) }.
% 0.93/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.58 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.93/1.58 ) ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.93/1.58 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.93/1.58 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__semidom( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__semidom( X ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.58 c_Groups_Oone__class_Oone( X ) ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.93/1.58 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.93/1.58 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.58 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.58 ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.93/1.58 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.58 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.93/1.58 ( X, Y ), Y ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__semidom( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.93/1.58 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__semidom( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.93/1.58 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.58 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.93/1.58 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.58 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha25( X, Y, Z ), alpha47
% 0.93/1.58 ( X, Y, Z ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha25( X, Y, Z
% 0.93/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.93/1.58 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha47( X, Y, Z
% 0.93/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.93/1.58 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.93/1.58 { ! alpha47( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.58 { ! alpha47( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.93/1.58 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ), alpha47( X, Y, Z ) }.
% 0.93/1.58 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.93/1.58 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), Y ), alpha25( X, Y, Z ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.93/1.58 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha26( X, Y, Z ), alpha48
% 0.93/1.58 ( X, Y, Z ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha26( X, Y, Z
% 0.93/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.93/1.58 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha48( X, Y, Z
% 0.93/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.93/1.58 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.58 { ! alpha48( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.58 { ! alpha48( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.93/1.58 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( X ), Y ), alpha48( X, Y, Z ) }.
% 0.93/1.58 { ! alpha26( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.93/1.58 { ! alpha26( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ) ), alpha26( X, Y, Z ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.93/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.93/1.58 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.93/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.93/1.58 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__semidom( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.93/1.58 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.58 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__semidom( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.93/1.58 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.58 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.58 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.93/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.93/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.93/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.58 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.58 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.58 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.58 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.58 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.93/1.58 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.93/1.58 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.93/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.58 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.93/1.58 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.58 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.93/1.58 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.93/1.58 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.93/1.58 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.93/1.58 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.93/1.58 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.93/1.58 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.93/1.58 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.93/1.58 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.93/1.58 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.93/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.93/1.58 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__semidom( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.93/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.93/1.58 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.58 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.93/1.58 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.93/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.93/1.58 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.93/1.58 .
% 0.93/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.58 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.58 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.58 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.58 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.58 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.58 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.58 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.58 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.58 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.93/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.93/1.58 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.93/1.58 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.93/1.58 , Y, T ) ) }.
% 0.93/1.58 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.93/1.58 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.93/1.58 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.93/1.58 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.58 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.93/1.58 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 0.93/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.93/1.58 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.93/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.93/1.58 tc_Nat_Onat, Y, X ), Y ) }.
% 0.93/1.58 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.93/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.93/1.58 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.93/1.58 tc_Nat_Onat, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y
% 0.93/1.58 ) ) }.
% 0.93/1.58 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) =
% 0.93/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.93/1.58 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.93/1.58 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.58 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.58 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.58 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.58 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.58 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.93/1.58 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.58 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.93/1.58 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.93/1.58 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.58 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.93/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.93/1.58 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.93/1.58 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.93/1.58 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.93/1.58 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.93/1.58 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.93/1.58 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.93/1.58 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.93/1.58 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.93/1.58 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.93/1.58 tc_Int_Oint ) }.
% 0.93/1.58 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.93/1.58 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.93/1.58 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.93/1.58 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.93/1.58 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.93/1.58 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.93/1.58 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.93/1.58 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.93/1.58 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.93/1.58 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.93/1.58 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.93/1.58 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.93/1.58 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.93/1.58 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.93/1.58 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.93/1.58 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.93/1.58 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.93/1.58 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.93/1.58 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.93/1.58 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.93/1.58 { class_Power_Opower( tc_Int_Oint ) }.
% 0.93/1.58 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.93/1.58 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.93/1.58 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.93/1.58 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.93/1.58 tc_Nat_Onat ) }.
% 0.93/1.58 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.93/1.58 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.93/1.58 tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.93/1.58 { ! class_Rings_Oidom( X ),
% 0.93/1.58 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.93/1.58 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.93/1.58 ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.93/1.58 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.93/1.58 X ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.93/1.58 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.93/1.58 ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.93/1.58 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.93/1.58 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.93/1.58 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.93/1.58 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.93/1.58 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.93/1.58 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.93/1.58 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.93/1.58 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.93/1.58 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.93/1.58 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.93/1.58 ( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.93/1.58 ( tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 0.93/1.58 ( X ) ) }.
% 0.93/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.93/1.58 }.
% 0.93/1.58 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.93/1.58 ) ) }.
% 0.93/1.58 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.93/1.58 .
% 0.93/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.93/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.93/1.58 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 0.93/1.58 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 0.93/1.58 { ! hBOOL( c_fFalse ) }.
% 0.93/1.58 { hBOOL( c_fTrue ) }.
% 0.93/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ),
% 0.93/1.58 v_p, c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.93/1.58 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), v_q ) ) }.
% 0.93/1.58
% 0.93/1.58 *** allocated 15000 integers for clauses
% 0.93/1.58 *** allocated 22500 integers for clauses
% 0.93/1.58 *** allocated 33750 integers for clauses
% 0.93/1.58 *** allocated 50625 integers for clauses
% 0.93/1.58 *** allocated 75937 integers for clauses
% 0.93/1.58 *** allocated 113905 integers for clauses
% 0.93/1.58 percentage equality = 0.323553, percentage horn = 0.876361
% 0.93/1.58 This is a problem with some equality
% 0.93/1.58
% 0.93/1.58
% 0.93/1.58
% 0.93/1.58 Options Used:
% 0.93/1.58
% 0.93/1.58 useres = 1
% 0.93/1.58 useparamod = 1
% 0.93/1.58 useeqrefl = 1
% 0.93/1.58 useeqfact = 1
% 0.93/1.58 usefactor = 1
% 0.93/1.58 usesimpsplitting = 0
% 0.93/1.58 usesimpdemod = 5
% 0.93/1.58 usesimpres = 3
% 0.93/1.58
% 0.93/1.58 resimpinuse = 1000
% 0.93/1.58 resimpclauses = 20000
% 0.93/1.58 substype = eqrewr
% 0.93/1.58 backwardsubs = 1
% 0.93/1.58 selectoldest = 5
% 0.93/1.58
% 0.93/1.58 litorderings [0] = split
% 0.93/1.58 litorderings [1] = extend the termordering, first sorting on arguments
% 0.93/1.58
% 0.93/1.58 termordering = kbo
% 0.93/1.58
% 0.93/1.58 litapriori = 0
% 0.93/1.58 termapriori = 1
% 0.93/1.58 litaposteriori = 0
% 0.93/1.58 termaposteriori = 0
% 0.93/1.58 demodaposteriori = 0
% 0.93/1.58 ordereqreflfact = 0
% 0.93/1.58
% 0.93/1.58 litselect = negord
% 0.93/1.58
% 0.93/1.58 maxweight = 15
% 0.93/1.58 maxdepth = 30000
% 0.93/1.58 maxlength = 115
% 0.93/1.58 maxnrvars = 195
% 0.93/1.58 excuselevel = 1
% 0.93/1.58 increasemaxweight = 1
% 0.93/1.58
% 0.93/1.58 maxselected = 10000000
% 0.93/1.58 maxnrclauses = 10000000
% 0.93/1.58
% 0.93/1.58 showgenerated = 0
% 0.93/1.58 showkept = 0
% 0.93/1.58 showselected = 0
% 0.93/1.58 showdeleted = 0
% 0.93/1.58 showresimp = 1
% 0.93/1.58 showstatus = 2000
% 0.93/1.58
% 0.93/1.58 prologoutput = 0
% 0.93/1.58 nrgoals = 5000000
% 0.93/1.58 totalproof = 1
% 0.93/1.58
% 0.93/1.58 Symbols occurring in the translation:
% 0.93/1.58
% 0.93/1.58 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.93/1.58 . [1, 2] (w:1, o:182, a:1, s:1, b:0),
% 0.93/1.58 ! [4, 1] (w:0, o:101, a:1, s:1, b:0),
% 0.93/1.58 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.93/1.58 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.93/1.58 hAPP [38, 2] (w:1, o:206, a:1, s:1, b:0),
% 0.93/1.58 tc_Complex_Ocomplex [39, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.93/1.58 tc_Polynomial_Opoly [40, 1] (w:1, o:109, a:1, s:1, b:0),
% 0.93/1.58 v_p [41, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.93/1.58 v_q [42, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.93/1.58 c_Rings_Odvd__class_Odvd [43, 3] (w:1, o:235, a:1, s:1, b:0),
% 0.93/1.58 class_Rings_Ocomm__semiring__1 [46, 1] (w:1, o:113, a:1, s:1, b:0),
% 0.93/1.58 c_Groups_Ozero__class_Ozero [47, 1] (w:1, o:114, a:1, s:1, b:0),
% 0.93/1.58 class_Groups_Ozero [48, 1] (w:1, o:119, a:1, s:1, b:0),
% 0.93/1.58 c_Polynomial_OpCons [49, 3] (w:1, o:239, a:1, s:1, b:0),
% 0.93/1.58 c_Polynomial_Opoly [59, 2] (w:1, o:207, a:1, s:1, b:0),
% 0.93/1.58 c_Polynomial_Opoly__rec [62, 5] (w:1, o:321, a:1, s:1, b:0),
% 0.93/1.58 class_Fields_Ofield [63, 1] (w:1, o:115, a:1, s:1, b:0),
% 0.93/1.58 c_Polynomial_Osmult [64, 3] (w:1, o:240, a:1, s:1, b:0),
% 0.93/1.58 class_Rings_Ocomm__semiring__0 [65, 1] (w:1, o:112, a:1, s:1, b:0),
% 0.93/1.58 class_Int_Oring__char__0 [66, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.93/1.58 class_Rings_Oidom [67, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.93/1.58 c_fequal [68, 2] (w:1, o:208, a:1, s:1, b:0),
% 0.93/1.58 c_If [69, 4] (w:1, o:295, a:1, s:1, b:0),
% 0.93/1.58 c_Polynomial_Oorder [72, 3] (w:1, o:238, a:1, s:1, b:0),
% 0.93/1.58 tc_Nat_Onat [73, 0] (w:1, o:41, a:1, s:1, b:0),
% 0.93/1.58 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [75, 3] (w:1
% 0.93/1.58 , o:241, a:1, s:1, b:0),
% 0.93/1.58 c_Polynomial_Osynthetic__div [76, 3] (w:1, o:242, a:1, s:1, b:0),
% 0.93/1.58 c_Groups_Oone__class_Oone [77, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.93/1.58 c_Groups_Oplus__class_Oplus [78, 3] (w:1, o:244, a:1, s:1, b:0),
% 0.93/1.58 c_Polynomial_Opcompose [79, 3] (w:1, o:245, a:1, s:1, b:0),
% 0.93/1.58 c_Polynomial_Omonom [80, 3] (w:1, o:246, a:1, s:1, b:0),
% 0.93/1.58 hBOOL [82, 1] (w:1, o:123, a:1, s:1, b:0),
% 0.93/1.58 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [87, 2] (w:1, o:209
% 0.93/1.58 , a:1, s:1, b:0),
% 0.93/1.58 class_Groups_Oone [88, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.93/1.58 class_Groups_Oab__semigroup__add [89, 1] (w:1, o:125, a:1, s:1, b:0)
% 0.93/1.58 ,
% 0.93/1.58 class_Groups_Ocancel__semigroup__add [91, 1] (w:1, o:126, a:1, s:1
% 0.93/1.58 , b:0),
% 0.93/1.58 class_Groups_Ocomm__monoid__add [92, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.93/1.58
% 0.93/1.58 class_Groups_Ocancel__ab__semigroup__add [93, 1] (w:1, o:128, a:1, s:
% 0.93/1.58 1, b:0),
% 0.93/1.58 class_Groups_Omonoid__add [94, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.93/1.58 class_Groups_Olinordered__ab__group__add [95, 1] (w:1, o:129, a:1, s:
% 0.93/1.58 1, b:0),
% 0.93/1.58 class_Rings_Ozero__neq__one [96, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.93/1.58 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [99
% 0.93/1.58 , 1] (w:1, o:161, a:1, s:1, b:0),
% 0.93/1.58 c_Groups_Ouminus__class_Ouminus [100, 2] (w:1, o:210, a:1, s:1, b:0)
% 0.93/1.58 ,
% 0.93/1.58 c_Groups_Otimes__class_Otimes [101, 1] (w:1, o:162, a:1, s:1, b:0),
% 0.93/1.58 c_Nat_OSuc [102, 1] (w:1, o:163, a:1, s:1, b:0),
% 0.93/1.58 class_Rings_Ocomm__ring__1 [104, 1] (w:1, o:110, a:1, s:1, b:0),
% 0.93/1.58 class_Groups_Oab__semigroup__mult [109, 1] (w:1, o:164, a:1, s:1, b:0
% 0.93/1.58 ),
% 0.93/1.58 class_Rings_Oring [110, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.93/1.58 class_Groups_Ogroup__add [111, 1] (w:1, o:165, a:1, s:1, b:0),
% 0.93/1.58 class_Rings_Oring__1__no__zero__divisors [112, 1] (w:1, o:133, a:1
% 0.93/1.58 , s:1, b:0),
% 0.93/1.58 class_Groups_Oab__group__add [113, 1] (w:1, o:166, a:1, s:1, b:0),
% 0.93/1.58 class_Rings_Ocomm__ring [114, 1] (w:1, o:111, a:1, s:1, b:0),
% 0.93/1.58 class_Rings_Ono__zero__divisors [119, 1] (w:1, o:142, a:1, s:1, b:0)
% 0.93/1.58 ,
% 0.93/1.58 class_Rings_Oring__no__zero__divisors [120, 1] (w:1, o:143, a:1, s:1
% 0.93/1.58 , b:0),
% 0.93/1.58 class_Rings_Omult__zero [121, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.93/1.58 class_Rings_Osemiring [123, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.93/1.58 class_Rings_Ocomm__semiring [124, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.93/1.58 class_Groups_Ocomm__monoid__mult [125, 1] (w:1, o:167, a:1, s:1, b:0)
% 0.93/1.58 ,
% 0.93/1.58 class_Groups_Omonoid__mult [126, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.93/1.58 class_Rings_Odvd [128, 1] (w:1, o:147, a:1, s:1, b:0),
% 0.93/1.58 class_Rings_Osemiring__0 [131, 1] (w:1, o:148, a:1, s:1, b:0),
% 0.93/1.58 class_Rings_Olinordered__ring__strict [133, 1] (w:1, o:134, a:1, s:1
% 0.93/1.58 , b:0),
% 0.93/1.58 c_Power_Opower__class_Opower [134, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.93/1.58 class_Rings_Oring__1 [140, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.93/1.58 class_Power_Opower [141, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.93/1.58 tc_Int_Oint [142, 0] (w:1, o:73, a:1, s:1, b:0),
% 0.93/1.58 c_Power_Opower_Opower [143, 3] (w:1, o:247, a:1, s:1, b:0),
% 0.93/1.58 class_RealVector_Oreal__normed__algebra [147, 1] (w:1, o:149, a:1, s:
% 0.93/1.58 1, b:0),
% 0.93/1.58 c_Polynomial_Odegree [159, 2] (w:1, o:212, a:1, s:1, b:0),
% 0.93/1.58 c_Groups_Ominus__class_Ominus [160, 3] (w:1, o:248, a:1, s:1, b:0),
% 0.93/1.58 c_Nat_Onat_Onat__size [162, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.93/1.58 c_Polynomial_Ocoeff [163, 2] (w:1, o:211, a:1, s:1, b:0),
% 0.93/1.58 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [168, 3] (w:1
% 0.93/1.58 , o:243, a:1, s:1, b:0),
% 0.93/1.58 c_Nat_Osize__class_Osize [169, 2] (w:1, o:213, a:1, s:1, b:0),
% 0.93/1.58 c_Polynomial_Opoly__gcd [171, 3] (w:1, o:249, a:1, s:1, b:0),
% 0.93/1.58 c_Orderings_Oord__class_Oless [172, 3] (w:1, o:236, a:1, s:1, b:0),
% 0.93/1.58 c_fTrue [173, 0] (w:1, o:94, a:1, s:1, b:0),
% 0.93/1.58 c_HOL_Obool_Obool__size [174, 1] (w:1, o:172, a:1, s:1, b:0),
% 0.93/1.58 class_Groups_Oordered__ab__semigroup__add__imp__le [175, 1] (w:1, o:
% 0.93/1.58 173, a:1, s:1, b:0),
% 0.93/1.58 class_Groups_Oordered__cancel__ab__semigroup__add [176, 1] (w:1, o:
% 0.93/1.58 174, a:1, s:1, b:0),
% 0.93/1.58 class_Groups_Oordered__ab__group__add [177, 1] (w:1, o:175, a:1, s:1
% 0.93/1.58 , b:0),
% 0.93/1.58 class_Rings_Olinordered__idom [181, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.93/1.58 class_Rings_Olinordered__semidom [183, 1] (w:1, o:137, a:1, s:1, b:0)
% 0.93/1.58 ,
% 0.93/1.58 class_Rings_Olinordered__ring [184, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.93/1.58 class_Rings_Olinordered__semiring__strict [185, 1] (w:1, o:138, a:1
% 0.93/1.58 , s:1, b:0),
% 0.93/1.58 class_Rings_Olinordered__comm__semiring__strict [186, 1] (w:1, o:139
% 0.93/1.58 , a:1, s:1, b:0),
% 0.93/1.58 class_Groups_Oordered__comm__monoid__add [187, 1] (w:1, o:176, a:1
% 0.93/1.58 , s:1, b:0),
% 0.93/1.58 class_Rings_Oordered__ring [192, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.93/1.58 c_fFalse [194, 0] (w:1, o:97, a:1, s:1, b:0),
% 0.93/1.58 c_Polynomial_Opdivmod__rel [196, 5] (w:1, o:322, a:1, s:1, b:0),
% 0.93/1.58 c_Rings_Oinverse__class_Odivide [203, 3] (w:1, o:250, a:1, s:1, b:0)
% 0.93/1.58 ,
% 0.93/1.58 class_Rings_Odivision__ring [204, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.93/1.58 class_RealVector_Oreal__normed__field [205, 1] (w:1, o:152, a:1, s:1
% 0.93/1.58 , b:0),
% 0.93/1.58 class_Fields_Ofield__inverse__zero [206, 1] (w:1, o:116, a:1, s:1, b:
% 0.93/1.58 0),
% 0.93/1.58 class_Rings_Odivision__ring__inverse__zero [207, 1] (w:1, o:153, a:1
% 0.93/1.58 , s:1, b:0),
% 0.93/1.58 class_RealVector_Oreal__field [208, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.93/1.58 class_Fields_Olinordered__field [209, 1] (w:1, o:117, a:1, s:1, b:0)
% 0.93/1.58 ,
% 0.93/1.58 class_Fields_Olinordered__field__inverse__zero [210, 1] (w:1, o:118
% 0.93/1.58 , a:1, s:1, b:0),
% 0.93/1.58 c_Divides_Odiv__class_Omod [211, 3] (w:1, o:251, a:1, s:1, b:0),
% 0.93/1.58 c_Polynomial_Opos__poly [212, 2] (w:1, o:214, a:1, s:1, b:0),
% 0.93/1.58 class_Divides_Osemiring__div [213, 1] (w:1, o:178, a:1, s:1, b:0),
% 0.93/1.58 class_Divides_Oring__div [217, 1] (w:1, o:177, a:1, s:1, b:0),
% 0.93/1.58 c_Divides_Odiv__class_Odiv [218, 3] (w:1, o:252, a:1, s:1, b:0),
% 0.93/1.58 c_Groups_Osgn__class_Osgn [219, 2] (w:1, o:215, a:1, s:1, b:0),
% 0.93/1.58 c_Rings_Oinverse__class_Oinverse [220, 2] (w:1, o:216, a:1, s:1, b:0)
% 0.93/1.58 ,
% 0.93/1.58 class_RealVector_Oreal__normed__div__algebra [221, 1] (w:1, o:155, a:
% 0.93/1.58 1, s:1, b:0),
% 0.93/1.58 class_RealVector_Oreal__normed__algebra__1 [222, 1] (w:1, o:156, a:1
% 0.93/1.58 , s:1, b:0),
% 0.93/1.58 class_RealVector_Oreal__normed__vector [223, 1] (w:1, o:157, a:1, s:1
% 0.93/1.58 , b:0),
% 0.93/1.58 class_Groups_Osgn__if [224, 1] (w:1, o:179, a:1, s:1, b:0),
% 0.93/1.58 c_Orderings_Oord__class_Oless__eq [225, 3] (w:1, o:237, a:1, s:1, b:0
% 0.93/1.58 ),
% 0.93/1.58 class_Rings_Oordered__cancel__semiring [226, 1] (w:1, o:158, a:1, s:1
% 0.93/1.58 , b:0),
% 0.93/1.58 class_Rings_Oordered__semiring [227, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.93/1.58
% 4.05/4.40 class_Rings_Oordered__comm__semiring [228, 1] (w:1, o:160, a:1, s:1
% 4.05/4.40 , b:0),
% 4.05/4.40 class_Groups_Oordered__ab__semigroup__add [229, 1] (w:1, o:180, a:1
% 4.05/4.40 , s:1, b:0),
% 4.05/4.40 class_Rings_Olinordered__semiring [232, 1] (w:1, o:140, a:1, s:1, b:0
% 4.05/4.40 ),
% 4.05/4.40 class_Groups_Ocancel__comm__monoid__add [234, 1] (w:1, o:181, a:1, s:
% 4.05/4.40 1, b:0),
% 4.05/4.40 alpha1 [235, 3] (w:1, o:253, a:1, s:1, b:1),
% 4.05/4.40 alpha2 [236, 2] (w:1, o:217, a:1, s:1, b:1),
% 4.05/4.40 alpha3 [237, 2] (w:1, o:220, a:1, s:1, b:1),
% 4.05/4.40 alpha4 [238, 2] (w:1, o:222, a:1, s:1, b:1),
% 4.05/4.40 alpha5 [239, 2] (w:1, o:223, a:1, s:1, b:1),
% 4.05/4.40 alpha6 [240, 2] (w:1, o:224, a:1, s:1, b:1),
% 4.05/4.40 alpha7 [241, 4] (w:1, o:299, a:1, s:1, b:1),
% 4.05/4.40 alpha8 [242, 4] (w:1, o:300, a:1, s:1, b:1),
% 4.05/4.40 alpha9 [243, 2] (w:1, o:225, a:1, s:1, b:1),
% 4.05/4.40 alpha10 [244, 3] (w:1, o:254, a:1, s:1, b:1),
% 4.05/4.40 alpha11 [245, 3] (w:1, o:255, a:1, s:1, b:1),
% 4.05/4.40 alpha12 [246, 3] (w:1, o:256, a:1, s:1, b:1),
% 4.05/4.40 alpha13 [247, 3] (w:1, o:257, a:1, s:1, b:1),
% 4.05/4.40 alpha14 [248, 3] (w:1, o:258, a:1, s:1, b:1),
% 4.05/4.40 alpha15 [249, 3] (w:1, o:259, a:1, s:1, b:1),
% 4.05/4.40 alpha16 [250, 3] (w:1, o:260, a:1, s:1, b:1),
% 4.05/4.40 alpha17 [251, 3] (w:1, o:261, a:1, s:1, b:1),
% 4.05/4.40 alpha18 [252, 3] (w:1, o:262, a:1, s:1, b:1),
% 4.05/4.40 alpha19 [253, 3] (w:1, o:263, a:1, s:1, b:1),
% 4.05/4.40 alpha20 [254, 3] (w:1, o:264, a:1, s:1, b:1),
% 4.05/4.40 alpha21 [255, 4] (w:1, o:301, a:1, s:1, b:1),
% 4.05/4.40 alpha22 [256, 4] (w:1, o:302, a:1, s:1, b:1),
% 4.05/4.40 alpha23 [257, 3] (w:1, o:265, a:1, s:1, b:1),
% 4.05/4.40 alpha24 [258, 3] (w:1, o:266, a:1, s:1, b:1),
% 4.05/4.40 alpha25 [259, 3] (w:1, o:267, a:1, s:1, b:1),
% 4.05/4.40 alpha26 [260, 3] (w:1, o:268, a:1, s:1, b:1),
% 4.05/4.40 alpha27 [261, 4] (w:1, o:303, a:1, s:1, b:1),
% 4.05/4.40 alpha28 [262, 2] (w:1, o:218, a:1, s:1, b:1),
% 4.05/4.40 alpha29 [263, 2] (w:1, o:219, a:1, s:1, b:1),
% 4.05/4.40 alpha30 [264, 2] (w:1, o:221, a:1, s:1, b:1),
% 4.05/4.40 alpha31 [265, 4] (w:1, o:304, a:1, s:1, b:1),
% 4.05/4.40 alpha32 [266, 4] (w:1, o:305, a:1, s:1, b:1),
% 4.05/4.40 alpha33 [267, 3] (w:1, o:269, a:1, s:1, b:1),
% 4.05/4.40 alpha34 [268, 3] (w:1, o:270, a:1, s:1, b:1),
% 4.05/4.40 alpha35 [269, 3] (w:1, o:271, a:1, s:1, b:1),
% 4.05/4.40 alpha36 [270, 3] (w:1, o:272, a:1, s:1, b:1),
% 4.05/4.40 alpha37 [271, 3] (w:1, o:273, a:1, s:1, b:1),
% 4.05/4.40 alpha38 [272, 4] (w:1, o:306, a:1, s:1, b:1),
% 4.05/4.40 alpha39 [273, 4] (w:1, o:307, a:1, s:1, b:1),
% 4.05/4.40 alpha40 [274, 4] (w:1, o:308, a:1, s:1, b:1),
% 4.05/4.40 alpha41 [275, 4] (w:1, o:309, a:1, s:1, b:1),
% 4.05/4.40 alpha42 [276, 3] (w:1, o:274, a:1, s:1, b:1),
% 4.05/4.40 alpha43 [277, 4] (w:1, o:310, a:1, s:1, b:1),
% 4.05/4.40 alpha44 [278, 4] (w:1, o:311, a:1, s:1, b:1),
% 4.05/4.40 alpha45 [279, 3] (w:1, o:275, a:1, s:1, b:1),
% 4.05/4.40 alpha46 [280, 3] (w:1, o:276, a:1, s:1, b:1),
% 4.05/4.40 alpha47 [281, 3] (w:1, o:277, a:1, s:1, b:1),
% 4.05/4.40 alpha48 [282, 3] (w:1, o:278, a:1, s:1, b:1),
% 4.05/4.40 alpha49 [283, 4] (w:1, o:312, a:1, s:1, b:1),
% 4.05/4.40 alpha50 [284, 3] (w:1, o:279, a:1, s:1, b:1),
% 4.05/4.40 alpha51 [285, 4] (w:1, o:313, a:1, s:1, b:1),
% 4.05/4.40 alpha52 [286, 4] (w:1, o:314, a:1, s:1, b:1),
% 4.05/4.40 alpha53 [287, 3] (w:1, o:280, a:1, s:1, b:1),
% 4.05/4.40 alpha54 [288, 4] (w:1, o:315, a:1, s:1, b:1),
% 4.05/4.40 alpha55 [289, 4] (w:1, o:316, a:1, s:1, b:1),
% 4.05/4.40 alpha56 [290, 4] (w:1, o:317, a:1, s:1, b:1),
% 4.05/4.40 alpha57 [291, 4] (w:1, o:318, a:1, s:1, b:1),
% 4.05/4.40 alpha58 [292, 4] (w:1, o:319, a:1, s:1, b:1),
% 4.05/4.40 alpha59 [293, 3] (w:1, o:281, a:1, s:1, b:1),
% 4.05/4.40 alpha60 [294, 3] (w:1, o:282, a:1, s:1, b:1),
% 4.05/4.40 alpha61 [295, 3] (w:1, o:283, a:1, s:1, b:1),
% 4.05/4.40 alpha62 [296, 4] (w:1, o:296, a:1, s:1, b:1),
% 4.05/4.40 alpha63 [297, 4] (w:1, o:297, a:1, s:1, b:1),
% 4.05/4.40 alpha64 [298, 4] (w:1, o:298, a:1, s:1, b:1),
% 4.05/4.40 skol1 [299, 2] (w:1, o:226, a:1, s:1, b:1),
% 4.05/4.40 skol2 [300, 2] (w:1, o:230, a:1, s:1, b:1),
% 4.05/4.40 skol3 [301, 3] (w:1, o:287, a:1, s:1, b:1),
% 4.05/4.40 skol4 [302, 2] (w:1, o:231, a:1, s:1, b:1),
% 4.05/4.40 skol5 [303, 3] (w:1, o:288, a:1, s:1, b:1),
% 4.05/4.40 skol6 [304, 2] (w:1, o:232, a:1, s:1, b:1),
% 4.05/4.40 skol7 [305, 1] (w:1, o:106, a:1, s:1, b:1),
% 4.05/4.40 skol8 [306, 1] (w:1, o:107, a:1, s:1, b:1),
% 36.14/36.49 skol9 [307, 2] (w:1, o:233, a:1, s:1, b:1),
% 36.14/36.49 skol10 [308, 2] (w:1, o:227, a:1, s:1, b:1),
% 36.14/36.49 skol11 [309, 3] (w:1, o:289, a:1, s:1, b:1),
% 36.14/36.49 skol12 [310, 3] (w:1, o:290, a:1, s:1, b:1),
% 36.14/36.49 skol13 [311, 4] (w:1, o:320, a:1, s:1, b:1),
% 36.14/36.49 skol14 [312, 2] (w:1, o:228, a:1, s:1, b:1),
% 36.14/36.49 skol15 [313, 2] (w:1, o:229, a:1, s:1, b:1),
% 36.14/36.49 skol16 [314, 3] (w:1, o:291, a:1, s:1, b:1),
% 36.14/36.49 skol17 [315, 3] (w:1, o:292, a:1, s:1, b:1),
% 36.14/36.49 skol18 [316, 3] (w:1, o:293, a:1, s:1, b:1),
% 36.14/36.49 skol19 [317, 3] (w:1, o:294, a:1, s:1, b:1),
% 36.14/36.49 skol20 [318, 2] (w:1, o:234, a:1, s:1, b:1),
% 36.14/36.49 skol21 [319, 3] (w:1, o:284, a:1, s:1, b:1),
% 36.14/36.49 skol22 [320, 1] (w:1, o:108, a:1, s:1, b:1),
% 36.14/36.49 skol23 [321, 3] (w:1, o:285, a:1, s:1, b:1),
% 36.14/36.49 skol24 [322, 3] (w:1, o:286, a:1, s:1, b:1).
% 36.14/36.49
% 36.14/36.49
% 36.14/36.49 Starting Search:
% 36.14/36.49
% 36.14/36.49 *** allocated 170857 integers for clauses
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49
% 36.14/36.49 Intermediate Status:
% 36.14/36.49 Generated: 2979
% 36.14/36.49 Kept: 2038
% 36.14/36.49 Inuse: 30
% 36.14/36.49 Deleted: 1
% 36.14/36.49 Deletedinuse: 0
% 36.14/36.49
% 36.14/36.49 *** allocated 256285 integers for clauses
% 36.14/36.49 *** allocated 170857 integers for termspace/termends
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49 *** allocated 384427 integers for clauses
% 36.14/36.49
% 36.14/36.49 Intermediate Status:
% 36.14/36.49 Generated: 6954
% 36.14/36.49 Kept: 4046
% 36.14/36.49 Inuse: 128
% 36.14/36.49 Deleted: 1
% 36.14/36.49 Deletedinuse: 0
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49 *** allocated 256285 integers for termspace/termends
% 36.14/36.49
% 36.14/36.49 Intermediate Status:
% 36.14/36.49 Generated: 12568
% 36.14/36.49 Kept: 6049
% 36.14/36.49 Inuse: 183
% 36.14/36.49 Deleted: 3
% 36.14/36.49 Deletedinuse: 0
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49 *** allocated 576640 integers for clauses
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49
% 36.14/36.49 Intermediate Status:
% 36.14/36.49 Generated: 17375
% 36.14/36.49 Kept: 8311
% 36.14/36.49 Inuse: 227
% 36.14/36.49 Deleted: 5
% 36.14/36.49 Deletedinuse: 1
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49 *** allocated 384427 integers for termspace/termends
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49
% 36.14/36.49 Intermediate Status:
% 36.14/36.49 Generated: 21809
% 36.14/36.49 Kept: 10328
% 36.14/36.49 Inuse: 262
% 36.14/36.49 Deleted: 5
% 36.14/36.49 Deletedinuse: 1
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49 *** allocated 864960 integers for clauses
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49
% 36.14/36.49 Intermediate Status:
% 36.14/36.49 Generated: 26725
% 36.14/36.49 Kept: 12861
% 36.14/36.49 Inuse: 306
% 36.14/36.49 Deleted: 8
% 36.14/36.49 Deletedinuse: 3
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49 *** allocated 576640 integers for termspace/termends
% 36.14/36.49
% 36.14/36.49 Intermediate Status:
% 36.14/36.49 Generated: 33144
% 36.14/36.49 Kept: 15066
% 36.14/36.49 Inuse: 335
% 36.14/36.49 Deleted: 9
% 36.14/36.49 Deletedinuse: 3
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49
% 36.14/36.49 Intermediate Status:
% 36.14/36.49 Generated: 40263
% 36.14/36.49 Kept: 17447
% 36.14/36.49 Inuse: 360
% 36.14/36.49 Deleted: 9
% 36.14/36.49 Deletedinuse: 3
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49 *** allocated 1297440 integers for clauses
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49
% 36.14/36.49 Intermediate Status:
% 36.14/36.49 Generated: 46164
% 36.14/36.49 Kept: 20165
% 36.14/36.49 Inuse: 405
% 36.14/36.49 Deleted: 9
% 36.14/36.49 Deletedinuse: 3
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49 Resimplifying clauses:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49
% 36.14/36.49 Intermediate Status:
% 36.14/36.49 Generated: 51363
% 36.14/36.49 Kept: 22176
% 36.14/36.49 Inuse: 453
% 36.14/36.49 Deleted: 344
% 36.14/36.49 Deletedinuse: 3
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49 *** allocated 864960 integers for termspace/termends
% 36.14/36.49
% 36.14/36.49 Intermediate Status:
% 36.14/36.49 Generated: 56345
% 36.14/36.49 Kept: 24224
% 36.14/36.49 Inuse: 474
% 36.14/36.49 Deleted: 344
% 36.14/36.49 Deletedinuse: 3
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49
% 36.14/36.49 Intermediate Status:
% 36.14/36.49 Generated: 60787
% 36.14/36.49 Kept: 26252
% 36.14/36.49 Inuse: 501
% 36.14/36.49 Deleted: 344
% 36.14/36.49 Deletedinuse: 3
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49 *** allocated 1946160 integers for clauses
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49
% 36.14/36.49 Intermediate Status:
% 36.14/36.49 Generated: 64790
% 36.14/36.49 Kept: 28441
% 36.14/36.49 Inuse: 520
% 36.14/36.49 Deleted: 344
% 36.14/36.49 Deletedinuse: 3
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49
% 36.14/36.49 Intermediate Status:
% 36.14/36.49 Generated: 70641
% 36.14/36.49 Kept: 30443
% 36.14/36.49 Inuse: 545
% 36.14/36.49 Deleted: 344
% 36.14/36.49 Deletedinuse: 3
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49 *** allocated 1297440 integers for termspace/termends
% 36.14/36.49
% 36.14/36.49 Intermediate Status:
% 36.14/36.49 Generated: 90528
% 36.14/36.49 Kept: 34031
% 36.14/36.49 Inuse: 590
% 36.14/36.49 Deleted: 344
% 36.14/36.49 Deletedinuse: 3
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49 Resimplifying inuse:
% 36.14/36.49 Done
% 36.14/36.49
% 36.14/36.49
% 36.14/36.49 Intermediate Status:
% 36.14/36.49 Generated: 99997
% 36.14/36.49 Kept: 36439
% 129.43/129.85 Inuse: 610
% 129.43/129.85 Deleted: 344
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 106285
% 129.43/129.85 Kept: 38518
% 129.43/129.85 Inuse: 625
% 129.43/129.85 Deleted: 344
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85 Resimplifying clauses:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 116666
% 129.43/129.85 Kept: 40637
% 129.43/129.85 Inuse: 645
% 129.43/129.85 Deleted: 409
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85 *** allocated 2919240 integers for clauses
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 124724
% 129.43/129.85 Kept: 42639
% 129.43/129.85 Inuse: 664
% 129.43/129.85 Deleted: 409
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 149339
% 129.43/129.85 Kept: 45423
% 129.43/129.85 Inuse: 685
% 129.43/129.85 Deleted: 409
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85 *** allocated 1946160 integers for termspace/termends
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 159773
% 129.43/129.85 Kept: 48727
% 129.43/129.85 Inuse: 720
% 129.43/129.85 Deleted: 409
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 163529
% 129.43/129.85 Kept: 50759
% 129.43/129.85 Inuse: 730
% 129.43/129.85 Deleted: 409
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 180760
% 129.43/129.85 Kept: 53584
% 129.43/129.85 Inuse: 775
% 129.43/129.85 Deleted: 409
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 195300
% 129.43/129.85 Kept: 55590
% 129.43/129.85 Inuse: 789
% 129.43/129.85 Deleted: 409
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 203308
% 129.43/129.85 Kept: 57679
% 129.43/129.85 Inuse: 825
% 129.43/129.85 Deleted: 409
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 211849
% 129.43/129.85 Kept: 59839
% 129.43/129.85 Inuse: 860
% 129.43/129.85 Deleted: 409
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85 Resimplifying clauses:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85 *** allocated 4378860 integers for clauses
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 243983
% 129.43/129.85 Kept: 63335
% 129.43/129.85 Inuse: 900
% 129.43/129.85 Deleted: 730
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 253554
% 129.43/129.85 Kept: 65340
% 129.43/129.85 Inuse: 926
% 129.43/129.85 Deleted: 730
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 264402
% 129.43/129.85 Kept: 68759
% 129.43/129.85 Inuse: 950
% 129.43/129.85 Deleted: 730
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85 *** allocated 2919240 integers for termspace/termends
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 273140
% 129.43/129.85 Kept: 70831
% 129.43/129.85 Inuse: 965
% 129.43/129.85 Deleted: 730
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 282118
% 129.43/129.85 Kept: 73045
% 129.43/129.85 Inuse: 980
% 129.43/129.85 Deleted: 730
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 294192
% 129.43/129.85 Kept: 75407
% 129.43/129.85 Inuse: 1020
% 129.43/129.85 Deleted: 730
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 306677
% 129.43/129.85 Kept: 78708
% 129.43/129.85 Inuse: 1050
% 129.43/129.85 Deleted: 730
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85 Resimplifying clauses:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 316046
% 129.43/129.85 Kept: 80718
% 129.43/129.85 Inuse: 1061
% 129.43/129.85 Deleted: 839
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 334582
% 129.43/129.85 Kept: 85181
% 129.43/129.85 Inuse: 1075
% 129.43/129.85 Deleted: 839
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 347258
% 129.43/129.85 Kept: 88080
% 129.43/129.85 Inuse: 1085
% 129.43/129.85 Deleted: 839
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 357102
% 129.43/129.85 Kept: 91290
% 129.43/129.85 Inuse: 1105
% 129.43/129.85 Deleted: 839
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 362096
% 129.43/129.85 Kept: 93606
% 129.43/129.85 Inuse: 1110
% 129.43/129.85 Deleted: 839
% 129.43/129.85 Deletedinuse: 3
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85 *** allocated 6568290 integers for clauses
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 373290
% 129.43/129.85 Kept: 95610
% 129.43/129.85 Inuse: 1143
% 129.43/129.85 Deleted: 840
% 129.43/129.85 Deletedinuse: 4
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85 Resimplifying inuse:
% 129.43/129.85 Done
% 129.43/129.85
% 129.43/129.85
% 129.43/129.85 Intermediate Status:
% 129.43/129.85 Generated: 381944
% 255.20/255.64 Kept: 97814
% 255.20/255.64 Inuse: 1165
% 255.20/255.64 Deleted: 840
% 255.20/255.64 Deletedinuse: 4
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 400735
% 255.20/255.64 Kept: 100174
% 255.20/255.64 Inuse: 1170
% 255.20/255.64 Deleted: 840
% 255.20/255.64 Deletedinuse: 4
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64 *** allocated 4378860 integers for termspace/termends
% 255.20/255.64 Resimplifying clauses:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 433612
% 255.20/255.64 Kept: 103520
% 255.20/255.64 Inuse: 1185
% 255.20/255.64 Deleted: 1174
% 255.20/255.64 Deletedinuse: 5
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 466515
% 255.20/255.64 Kept: 106620
% 255.20/255.64 Inuse: 1195
% 255.20/255.64 Deleted: 1174
% 255.20/255.64 Deletedinuse: 5
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 491085
% 255.20/255.64 Kept: 109757
% 255.20/255.64 Inuse: 1205
% 255.20/255.64 Deleted: 1174
% 255.20/255.64 Deletedinuse: 5
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 506507
% 255.20/255.64 Kept: 111816
% 255.20/255.64 Inuse: 1215
% 255.20/255.64 Deleted: 1174
% 255.20/255.64 Deletedinuse: 5
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 530318
% 255.20/255.64 Kept: 113817
% 255.20/255.64 Inuse: 1239
% 255.20/255.64 Deleted: 1174
% 255.20/255.64 Deletedinuse: 5
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 550797
% 255.20/255.64 Kept: 118705
% 255.20/255.64 Inuse: 1265
% 255.20/255.64 Deleted: 1175
% 255.20/255.64 Deletedinuse: 6
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 560810
% 255.20/255.64 Kept: 122411
% 255.20/255.64 Inuse: 1270
% 255.20/255.64 Deleted: 1175
% 255.20/255.64 Deletedinuse: 6
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64 Resimplifying clauses:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 567454
% 255.20/255.64 Kept: 125807
% 255.20/255.64 Inuse: 1275
% 255.20/255.64 Deleted: 1763
% 255.20/255.64 Deletedinuse: 7
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 580586
% 255.20/255.64 Kept: 129125
% 255.20/255.64 Inuse: 1280
% 255.20/255.64 Deleted: 1763
% 255.20/255.64 Deletedinuse: 7
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 595481
% 255.20/255.64 Kept: 131151
% 255.20/255.64 Inuse: 1307
% 255.20/255.64 Deleted: 1769
% 255.20/255.64 Deletedinuse: 8
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 608505
% 255.20/255.64 Kept: 134081
% 255.20/255.64 Inuse: 1310
% 255.20/255.64 Deleted: 1769
% 255.20/255.64 Deletedinuse: 8
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 621054
% 255.20/255.64 Kept: 140350
% 255.20/255.64 Inuse: 1315
% 255.20/255.64 Deleted: 1769
% 255.20/255.64 Deletedinuse: 8
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64 *** allocated 9852435 integers for clauses
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 634152
% 255.20/255.64 Kept: 147060
% 255.20/255.64 Inuse: 1340
% 255.20/255.64 Deleted: 1769
% 255.20/255.64 Deletedinuse: 8
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64 Resimplifying clauses:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 644671
% 255.20/255.64 Kept: 149236
% 255.20/255.64 Inuse: 1369
% 255.20/255.64 Deleted: 1858
% 255.20/255.64 Deletedinuse: 12
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 654065
% 255.20/255.64 Kept: 153216
% 255.20/255.64 Inuse: 1380
% 255.20/255.64 Deleted: 1858
% 255.20/255.64 Deletedinuse: 12
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 662145
% 255.20/255.64 Kept: 155685
% 255.20/255.64 Inuse: 1390
% 255.20/255.64 Deleted: 1858
% 255.20/255.64 Deletedinuse: 12
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 671950
% 255.20/255.64 Kept: 159889
% 255.20/255.64 Inuse: 1410
% 255.20/255.64 Deleted: 1858
% 255.20/255.64 Deletedinuse: 12
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 677076
% 255.20/255.64 Kept: 162557
% 255.20/255.64 Inuse: 1415
% 255.20/255.64 Deleted: 1858
% 255.20/255.64 Deletedinuse: 12
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 683280
% 255.20/255.64 Kept: 165365
% 255.20/255.64 Inuse: 1425
% 255.20/255.64 Deleted: 1858
% 255.20/255.64 Deletedinuse: 12
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 689016
% 255.20/255.64 Kept: 168851
% 255.20/255.64 Inuse: 1430
% 255.20/255.64 Deleted: 1858
% 255.20/255.64 Deletedinuse: 12
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64 Resimplifying clauses:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64 *** allocated 6568290 integers for termspace/termends
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 700660
% 255.20/255.64 Kept: 173288
% 255.20/255.64 Inuse: 1455
% 255.20/255.64 Deleted: 1932
% 255.20/255.64 Deletedinuse: 12
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 705908
% 255.20/255.64 Kept: 176028
% 255.20/255.64 Inuse: 1460
% 255.20/255.64 Deleted: 1932
% 255.20/255.64 Deletedinuse: 12
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 712298
% 255.20/255.64 Kept: 178934
% 255.20/255.64 Inuse: 1470
% 255.20/255.64 Deleted: 1932
% 255.20/255.64 Deletedinuse: 12
% 255.20/255.64
% 255.20/255.64 Resimplifying inuse:
% 255.20/255.64 Done
% 255.20/255.64
% 255.20/255.64
% 255.20/255.64 Intermediate Status:
% 255.20/255.64 Generated: 718144
% 255.20/255.64 KCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------