TSTP Solution File: SWW269+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW269+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n028.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 23:21:43 EDT 2022
% Result : Timeout 300.07s 300.45s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWW269+1 : TPTP v8.1.0. Released v5.2.0.
% 0.12/0.13 % Command : bliksem %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sun Jun 5 05:23:27 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.92/1.56 *** allocated 10000 integers for termspace/termends
% 0.92/1.56 *** allocated 10000 integers for clauses
% 0.92/1.56 *** allocated 10000 integers for justifications
% 0.92/1.56 *** allocated 15000 integers for termspace/termends
% 0.92/1.56 *** allocated 22500 integers for termspace/termends
% 0.92/1.56 *** allocated 33750 integers for termspace/termends
% 0.92/1.56 Bliksem 1.12
% 0.92/1.56
% 0.92/1.56
% 0.92/1.56 Automatic Strategy Selection
% 0.92/1.56
% 0.92/1.56 *** allocated 50625 integers for termspace/termends
% 0.92/1.56 *** allocated 75937 integers for termspace/termends
% 0.92/1.56 *** allocated 113905 integers for termspace/termends
% 0.92/1.56
% 0.92/1.56 Clauses:
% 0.92/1.56
% 0.92/1.56 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.92/1.56 { v_d____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.92/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.92/1.56 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.92/1.56 tc_Complex_Ocomplex, v_d____, v_ds____ ) ), X ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.92/1.56 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.92/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.92/1.56 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.92/1.56 { ! skol2 = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), v_ds____ =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.92/1.56 }.
% 0.92/1.56 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_ds____ ), skol2 ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), v_ds____ =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.92/1.56 }.
% 0.92/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), ! v_p =
% 0.92/1.56 c_Polynomial_OpCons( tc_Complex_Ocomplex, X, c_Groups_Ozero__class_Ozero
% 0.92/1.56 ( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.92/1.56 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.92/1.56 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.92/1.56 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.92/1.56 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.92/1.56 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.92/1.56 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.92/1.56 , hAPP( hAPP( c_fequal, Y ), c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ) ), U, c_Polynomial_Opoly__rec( W, X, U, T, Y )
% 0.92/1.56 ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.92/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { ! v_c____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.92/1.56 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.92/1.56 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.92/1.56 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.92/1.56 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.92/1.56 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.92/1.56 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.92/1.56 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.92/1.56 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), !
% 0.92/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 0.92/1.56 ( tc_Polynomial_Opoly( X ) ),
% 0.92/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.92/1.56 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_cs____ ), X ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.92/1.56 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.92/1.56 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.92/1.56 tc_Complex_Ocomplex, v_c____, v_cs____ ) ), c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Complex_Ocomplex ) ) = hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.92/1.56 c_Polynomial_OpCons( tc_Complex_Ocomplex, v_c____, v_cs____ ) ), X ) }.
% 0.92/1.56 { c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 0.92/1.56 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.92/1.56 c_Polynomial_OpCons( tc_Complex_Ocomplex, v_c____, v_cs____ ) ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.92/1.56 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.92/1.56 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.92/1.56 ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.92/1.56 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.92/1.56 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 0.92/1.56 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero
% 0.92/1.56 ( tc_Polynomial_Opoly( X ) ) ) ), hBOOL( hAPP( Y, skol3( Z, Y ) ) ),
% 0.92/1.56 hBOOL( hAPP( Y, T ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero
% 0.92/1.56 ( tc_Polynomial_Opoly( X ) ) ) ), ! hBOOL( hAPP( Y, c_Polynomial_OpCons(
% 0.92/1.56 X, skol25( X, Y ), skol3( X, Y ) ) ) ), hBOOL( hAPP( Y, Z ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.56 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), !
% 0.92/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ),
% 0.92/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.92/1.56 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.92/1.56 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.92/1.56 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 0.92/1.56 X, T ) = hAPP( X, U ) }.
% 0.92/1.56 { ! hAPP( X, skol4( X ) ) = hAPP( X, skol26( X ) ),
% 0.92/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { ! v_c____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.92/1.56 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.92/1.56 tc_Complex_Ocomplex, v_c____, v_cs____ ) ), skol5 ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.92/1.56 { c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 0.92/1.56 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex, X ) ),
% 0.92/1.56 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol6( X ) ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 0.92/1.56 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.56 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 0.92/1.56 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.92/1.56 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.92/1.56 }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 0.92/1.56 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 0.92/1.56 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.92/1.56 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ),
% 0.92/1.56 c_Polynomial_OpCons( X, Z, Y ) ) ), hBOOL( hAPP( hAPP(
% 0.92/1.56 c_HOL_Oequal__class_Oequal( X ), c_Groups_Ozero__class_Ozero( X ) ), Z )
% 0.92/1.56 ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.92/1.56 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ),
% 0.92/1.56 c_Polynomial_OpCons( X, Z, Y ) ) ), hBOOL( hAPP( hAPP(
% 0.92/1.56 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.92/1.56 c_HOL_Oequal__class_Oequal( X ), c_Groups_Ozero__class_Ozero( X ) ), Z )
% 0.92/1.56 ), ! hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly
% 0.92/1.56 ( X ) ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) )
% 0.92/1.56 , hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X )
% 0.92/1.56 ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ),
% 0.92/1.56 c_Polynomial_OpCons( X, Z, Y ) ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.92/1.56 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.92/1.56 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ) ) ), hBOOL( hAPP( hAPP(
% 0.92/1.56 c_HOL_Oequal__class_Oequal( X ), Z ), c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.56 ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.92/1.56 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.92/1.56 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ) ) ), hBOOL( hAPP( hAPP(
% 0.92/1.56 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ), Y ),
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.92/1.56 c_HOL_Oequal__class_Oequal( X ), Z ), c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.56 ), ! hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly
% 0.92/1.56 ( X ) ), Y ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) )
% 0.92/1.56 , hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X )
% 0.92/1.56 ), c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ) ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.92/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 0.92/1.56 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.92/1.56 , Y ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.92/1.56 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.92/1.56 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.56 }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 0.92/1.56 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.92/1.56 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Nat_Onat ) ) = Z }.
% 0.92/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 Y, T ), Z = Y }.
% 0.92/1.56 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 T, Y ), Z = Y }.
% 0.92/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 T, Y ), Z = Y }.
% 0.92/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 Y, Z ), T = Y }.
% 0.92/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 Y, Z ) }.
% 0.92/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 T, Y ), Z = Y }.
% 0.92/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 T, Y ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.92/1.56 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.92/1.56 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.92/1.56 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 0.92/1.56 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.92/1.56 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.92/1.56 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 0.92/1.56 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 0.92/1.56 c_Polynomial_Ocoeff( X, Y ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 0.92/1.56 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.92/1.56 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), Z = Y
% 0.92/1.56 }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! Z = Y, hBOOL( hAPP
% 0.92/1.56 ( hAPP( c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 0.92/1.56 ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 0.92/1.56 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol7( X
% 0.92/1.56 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol7( X, Y, Z ) ), Z = Y
% 0.92/1.56 }.
% 0.92/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.92/1.56 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.92/1.56 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 0.92/1.56 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.92/1.56 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.92/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.92/1.56 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.92/1.56 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.56 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.56 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.92/1.56 c_Polynomial_Odegree( X, Y ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.92/1.56 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.92/1.56 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.92/1.56 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.92/1.56 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.92/1.56 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.92/1.56 c_Polynomial_OpCons( X, U, T ) ), c_Polynomial_OpCons( X, Z, Y ) ) ),
% 0.92/1.56 hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal( X ), U ), Z ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.92/1.56 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.92/1.56 c_Polynomial_OpCons( X, U, T ) ), c_Polynomial_OpCons( X, Z, Y ) ) ),
% 0.92/1.56 hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) )
% 0.92/1.56 , T ), Y ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.92/1.56 c_HOL_Oequal__class_Oequal( X ), U ), Z ) ), ! hBOOL( hAPP( hAPP(
% 0.92/1.56 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ), T ), Y ) ), hBOOL
% 0.92/1.56 ( hAPP( hAPP( c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.92/1.56 c_Polynomial_OpCons( X, U, T ) ), c_Polynomial_OpCons( X, Z, Y ) ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.92/1.56 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.92/1.56 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.92/1.56 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.92/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.92/1.56 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.92/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.92/1.56 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.92/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.92/1.56 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 0.92/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 0.92/1.56 c_Polynomial_OpCons( X, T,
% 0.92/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 0.92/1.56 .
% 0.92/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.92/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.92/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) =
% 0.92/1.56 c_Polynomial_Odegree( X, Z ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.92/1.56 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.92/1.56 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ),
% 0.92/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ),
% 0.92/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 0.92/1.56 c_Polynomial_Odegree( X, Y ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 0.92/1.56 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 0.92/1.56 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 0.92/1.56 , Y ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.92/1.56 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 0.92/1.56 }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.92/1.56 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 0.92/1.56 ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), hBOOL( hAPP( hAPP(
% 0.92/1.56 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ),
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.56 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 0.92/1.56 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.56 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha1( X, Y ), alpha26
% 0.92/1.56 ( X, Y ) }.
% 0.92/1.56 { ! alpha1( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.92/1.56 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! alpha26( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.92/1.56 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! alpha26( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! alpha26( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Nat_Onat ) ) }.
% 0.92/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha26( X, Y ) }.
% 0.92/1.56 { ! alpha1( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Nat_Onat ) ) }.
% 0.92/1.56 { ! alpha1( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha1( X, Y ) }.
% 0.92/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha2( X, Y ), alpha27( X
% 0.92/1.56 , Y ) }.
% 0.92/1.56 { ! alpha2( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.92/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.92/1.56 { ! alpha27( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.92/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.92/1.56 { ! alpha27( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! alpha27( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Nat_Onat ) ) }.
% 0.92/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha27( X, Y ) }.
% 0.92/1.56 { ! alpha2( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Nat_Onat ) ) }.
% 0.92/1.56 { ! alpha2( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha2( X, Y ) }.
% 0.92/1.56 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.92/1.56 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.92/1.56 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.92/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.56 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.92/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.92/1.56 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.92/1.56 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.92/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.92/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.92/1.56 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.92/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.92/1.56 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.92/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.92/1.56 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.92/1.56 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.92/1.56 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.92/1.56 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.92/1.56 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.92/1.56 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.92/1.56 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.92/1.56 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.92/1.56 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.92/1.56 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.92/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Nat_Onat ), X ) = X }.
% 0.92/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.92/1.56 ( tc_Nat_Onat ) ) = X }.
% 0.92/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.92/1.56 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.92/1.56 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.92/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.92/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.92/1.56 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.92/1.56 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.56 { ! c_Nat_OSuc( X ) = X }.
% 0.92/1.56 { ! X = c_Nat_OSuc( X ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.92/1.56 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.92/1.56 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ), Y,
% 0.92/1.56 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.92/1.56 { c_Nat_Onat_Onat__size( c_Nat_OSuc( X ) ) = c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Nat_Onat, c_Nat_Onat_Onat__size( X ), c_Nat_OSuc(
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 tc_Polynomial_Opoly( X ), T, c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 0.92/1.56 c_Polynomial_Osmult( X, Z, T ), c_Polynomial_OpCons( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 tc_Polynomial_Opoly( X ), T, Y ) ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T, Z ), Y ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 0.92/1.56 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_OpCons( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 tc_Polynomial_Opoly( X ), Z, Y ) ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_Ocoeff( X, c_Polynomial_OpCons( X
% 0.92/1.56 , Z, Y ) ) = c_Nat_Onat_Onat__case( X, Z, c_Polynomial_Ocoeff( X, Y ) ) }
% 0.92/1.56 .
% 0.92/1.56 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_Osize__class_Osize(
% 0.92/1.56 tc_Nat_Onat, X ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.92/1.56 ) ) }.
% 0.92/1.56 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.92/1.56 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 0.92/1.56 ) }.
% 0.92/1.56 { ! class_HOL_Oequal( X ), c_fequal = c_HOL_Oequal__class_Oequal( X ) }.
% 0.92/1.56 { ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal
% 0.92/1.56 ( X ), Z ), Y ) ), Z = Y }.
% 0.92/1.56 { ! class_HOL_Oequal( X ), ! Z = Y, hBOOL( hAPP( hAPP(
% 0.92/1.56 c_HOL_Oequal__class_Oequal( X ), Z ), Y ) ) }.
% 0.92/1.56 { ! class_HOL_Oequal( X ), hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal( X
% 0.92/1.56 ), Y ), Y ) ) }.
% 0.92/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.92/1.56 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, Z, Y ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, U, Z ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, T, Y ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, Z, Y ) ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X, U, T
% 0.92/1.56 ), Y ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, Z, Y ) ) = c_Groups_Otimes__class_Otimes( X, U,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Otimes__class_Otimes( X, Z
% 0.92/1.56 , Y ) ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X, T, Y
% 0.92/1.56 ), Z ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Otimes__class_Otimes( X, Z
% 0.92/1.56 , Y ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.92/1.56 T, c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.92/1.56 ), Y ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.92/1.56 T, c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Z, c_Groups_Otimes__class_Otimes( X, T
% 0.92/1.56 , Y ) ) }.
% 0.92/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.92/1.56 Z, Y ) = c_Groups_Otimes__class_Otimes( X, Y, Z ) }.
% 0.92/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.92/1.56 { c_Nat_Osize__class_Osize( tc_Nat_Onat, X ) = X }.
% 0.92/1.56 { ! class_Groups_Oab__semigroup__mult( X ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Otimes__class_Otimes( X, Z
% 0.92/1.56 , Y ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.92/1.56 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.92/1.56 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, Y, Y ) ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, Y, Y ) ), c_Groups_Ozero__class_Ozero( X ) ), Z =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, Y, Y ) ), c_Groups_Ozero__class_Ozero( X ) ), Y =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.56 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, Y, Y ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.92/1.56 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Otimes__class_Otimes(
% 0.92/1.56 tc_Polynomial_Opoly( X ), Z, Y ) ), c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.92/1.56 ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, U, T ),
% 0.92/1.56 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Nat_Onat, T, Y ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.92/1.56 Y, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.56 }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.56 }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.92/1.56 T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.92/1.56 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.92/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.92/1.56 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, U, Z ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, T, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, U, Y ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, T, Z ) ) }.
% 0.92/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.92/1.56 ( X ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.56 U, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, U, Y )
% 0.92/1.56 , c_Groups_Otimes__class_Otimes( X, T, Z ) ), ! U = T }.
% 0.92/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.92/1.56 ( X ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.56 U, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, U, Y )
% 0.92/1.56 , c_Groups_Otimes__class_Otimes( X, T, Z ) ), ! Z = Y }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.92/1.56 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, T, Z ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, Y, Z ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.92/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.92/1.56 ( X ), ! c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.92/1.56 , U, T ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, U, Y )
% 0.92/1.56 , c_Groups_Otimes__class_Otimes( X, Z, T ) ), U = Z, T = Y }.
% 0.92/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.92/1.56 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, U, Y ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, Z, T ) ) }.
% 0.92/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.92/1.56 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, U, Y ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, Z, T ) ) }.
% 0.92/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.92/1.56 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.92/1.56 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.56 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.92/1.56 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.92/1.56 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.92/1.56 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.92/1.56 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.92/1.56 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.92/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.92/1.56 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.92/1.56 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.92/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.92/1.56 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.92/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.92/1.56 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.92/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.92/1.56 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Nat_Onat ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.92/1.56 .
% 0.92/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.92/1.56 ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.92/1.56 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.92/1.56 , c_Nat_OSuc( X ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.92/1.56 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.92/1.56 }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.92/1.56 c_Nat_OSuc( X ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.92/1.56 ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol8( X, Y ) ) }.
% 0.92/1.56 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.92/1.56 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 0.92/1.56 c_Polynomial_Osmult( X, T, c_Groups_Otimes__class_Otimes(
% 0.92/1.56 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.92/1.56 c_Polynomial_Osmult( X, Z, c_Groups_Otimes__class_Otimes(
% 0.92/1.56 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 tc_Polynomial_Opoly( X ), c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Polynomial_Opoly( X ), T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Polynomial_Opoly( X ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 tc_Polynomial_Opoly( X ), T, Y ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.92/1.56 { c_Nat_Onat_Onat__size( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ), Z, Y ) ),
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ),
% 0.92/1.56 c_Polynomial_Odegree( X, Y ) ) ) = c_Groups_Otimes__class_Otimes( X, hAPP
% 0.92/1.56 ( c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ), hAPP(
% 0.92/1.56 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z )
% 0.92/1.56 , c_Groups_Otimes__class_Otimes( X, Y, Y ) ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.92/1.56 .
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z )
% 0.92/1.56 , c_Groups_Otimes__class_Otimes( X, Y, Y ) ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.92/1.56 .
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.56 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z
% 0.92/1.56 ), c_Groups_Otimes__class_Otimes( X, Y, Y ) ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.92/1.56 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, W, c_Groups_Otimes__class_Otimes( X, Y, T
% 0.92/1.56 ) ) = c_Groups_Oplus__class_Oplus( X, U, c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, Y, Z ) ) }.
% 0.92/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.56 ) }.
% 0.92/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.92/1.56 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.92/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.92/1.56 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.56 ) }.
% 0.92/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.92/1.56 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.56 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.92/1.56 ) }.
% 0.92/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.56 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.92/1.56 .
% 0.92/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.56 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.92/1.56 .
% 0.92/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.56 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.92/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 Y, Z ) ) }.
% 0.92/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 Z, Y ) ) }.
% 0.92/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.92/1.56 ) ) }.
% 0.92/1.56 { hAPP( c_Nat_Onat_Onat__case( Z, Y, X ), c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Nat_Onat ) ) = Y }.
% 0.92/1.56 { hAPP( c_Nat_Onat_Onat__case( T, Z, Y ), c_Nat_OSuc( X ) ) = hAPP( Y, X )
% 0.92/1.56 }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.92/1.56 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, T, Z ), c_Polynomial_Osmult( X, T, Y )
% 0.92/1.56 ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.92/1.56 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Groups_Otimes__class_Otimes( X
% 0.92/1.56 , T, hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.92/1.56 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Groups_Otimes__class_Otimes( X
% 0.92/1.56 , T, hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.92/1.56 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) )
% 0.92/1.56 , c_Polynomial_Odegree( X, Y ) ) }.
% 0.92/1.56 { ! class_Groups_Ocomm__monoid__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.92/1.56 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.56 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 0.92/1.56 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.92/1.56 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.92/1.56 , c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Z, Y ) ), Y ) }.
% 0.92/1.56 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ), Y, Z ) ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 0.92/1.56 c_Polynomial_Odegree( X, Z ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.92/1.56 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.92/1.56 , c_Groups_Otimes__class_Otimes( X, Y, hAPP( c_Polynomial_Opoly( X, Z ),
% 0.92/1.56 Y ) ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.92/1.56 tc_Nat_Onat, Y, c_Polynomial_Odegree( X, Z ) ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.92/1.56 , c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Z, Y ) ), c_Nat_OSuc(
% 0.92/1.56 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.92/1.56 { ! class_HOL_Oequal( X ), c_HOL_Oequal__class_Oequal( X ) = c_fequal }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.92/1.56 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Y
% 0.92/1.56 , Y ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Z, Y ) ), alpha3( X, Y, Z ), alpha28( X
% 0.92/1.56 , Y, Z ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha28( X, Y, Z ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.92/1.56 { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.56 { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.92/1.56 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) ), alpha28( X, Y, Z ) }.
% 0.92/1.56 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.92/1.56 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.56 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), Y ), alpha3( X, Y, Z ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.92/1.56 , Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha4( X, Y, Z ), alpha29( X
% 0.92/1.56 , Y, Z ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.92/1.56 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha29( X, Y, Z ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.92/1.56 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.56 { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.56 { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.92/1.56 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.92/1.56 ( X ), Y ), alpha29( X, Y, Z ) }.
% 0.92/1.56 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.92/1.56 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.56 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) ), alpha4( X, Y, Z ) }.
% 0.92/1.56 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.56 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Y, Z
% 0.92/1.56 ) ) }.
% 0.92/1.56 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.56 , c_Groups_Otimes__class_Otimes( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.92/1.56 X ) ) }.
% 0.92/1.56 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.56 , c_Groups_Otimes__class_Otimes( X, Z, Y ), c_Groups_Ozero__class_Ozero(
% 0.92/1.56 X ) ) }.
% 0.92/1.56 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.56 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.92/1.56 ) ) }.
% 0.92/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.56 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.92/1.56 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.92/1.56 { ! class_Rings_Oordered__semiring( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.92/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, Z, T ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.92/1.56 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ), Y = X, Z =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! Y = X, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) }.
% 0.92/1.56 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) }.
% 0.92/1.56 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ), Z = X, Y =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! Z = X, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) }.
% 0.92/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) }.
% 0.92/1.56 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ) =
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ), Y = X }
% 0.92/1.56 .
% 0.92/1.56 { ! Y = X, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y )
% 0.92/1.56 = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ) }.
% 0.92/1.56 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.56 tc_Nat_Onat, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) )
% 0.92/1.56 }.
% 0.92/1.56 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, X ) ) }.
% 0.92/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, X ) ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, Z ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, T ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ) ) }.
% 0.92/1.56 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc(
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.92/1.56 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc(
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.92/1.56 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.92/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.92/1.56 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.56 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.92/1.56 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Opcompose( X, Z, Y )
% 0.92/1.56 ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.92/1.56 Z ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.92/1.56 { ! class_Rings_Omult__zero( X ), c_Groups_Otimes__class_Otimes( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.56 }.
% 0.92/1.56 { ! class_Rings_Omult__zero( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! class_Rings_Oring__no__zero__divisors( X ), !
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.92/1.56 ), Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.92/1.56 ( X ) }.
% 0.92/1.56 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.92/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.92/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 X ), Z = c_Groups_Ozero__class_Ozero( X ), !
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Y, Z ) = c_Groups_Ozero__class_Ozero( X
% 0.92/1.56 ) }.
% 0.92/1.56 { ! class_Rings_Ono__zero__divisors( X ), ! c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.92/1.56 .
% 0.92/1.56 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Oplus__class_Oplus( X
% 0.92/1.56 , c_Groups_Otimes__class_Otimes( X, Z, T ), Y ) ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, U, Z ), T ), Y ) }.
% 0.92/1.56 { ! class_Rings_Ocomm__semiring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.92/1.56 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.92/1.56 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.92/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.56 , c_Groups_Otimes__class_Otimes( X, Z, Y ), c_Groups_Ozero__class_Ozero(
% 0.92/1.56 X ) ) }.
% 0.92/1.56 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.56 X ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Z, Y ), c_Groups_Ozero__class_Ozero( X
% 0.92/1.56 ) ) }.
% 0.92/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.56 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.92/1.56 ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.92/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.56 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.92/1.56 ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.92/1.56 { ! class_Rings_Oordered__semiring( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.56 X ), U ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Z, U ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, Y, T ) ) }.
% 0.92/1.56 { ! class_Rings_Oordered__semiring( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.92/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.56 X ), U ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Z, U ), c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, Y, T ) ) }.
% 0.92/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.56 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.56 , c_Groups_Otimes__class_Otimes( X, T, Y ), c_Groups_Otimes__class_Otimes
% 0.92/1.56 ( X, T, Z ) ) }.
% 0.92/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.56 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.56 , c_Groups_Otimes__class_Otimes( X, Y, T ), c_Groups_Otimes__class_Otimes
% 0.92/1.56 ( X, Z, T ) ) }.
% 0.92/1.56 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.92/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.92/1.56 { ! class_Rings_Oordered__semiring( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.92/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes(
% 0.92/1.56 X, T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.92/1.56 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.92/1.56 , Y ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol9( X, Y ) ) }.
% 0.92/1.56 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.92/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.92/1.56 , Y ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.92/1.56 , T, Y ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.92/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.92/1.56 , Y ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.92/1.56 , T, Y ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.92/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.92/1.56 ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.56 T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.92/1.56 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Otimes__class_Otimes
% 0.92/1.56 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.92/1.56 Z, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.56 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) }.
% 0.92/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.92/1.56 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.92/1.56 hAPP( Y, U ) ) }.
% 0.92/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.92/1.56 ( Z, skol10( X, Y, Z ) ), hAPP( Y, skol10( X, Y, Z ) ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.56 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.92/1.56 ( X, Z, Y ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.92/1.56 ( X, Y, Z ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.56 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.92/1.56 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.92/1.56 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.92/1.56 hAPP( Y, U ) ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.56 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.56 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.92/1.56 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.92/1.56 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.92/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.92/1.56 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.56 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.56 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.92/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.56 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.56 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.56 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.92/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.92/1.56 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.92/1.56 hAPP( Y, U ) ) }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.56 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.92/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Y, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Y, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, c_Groups_Ozero__class_Ozero( X ), Y ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, c_Groups_Ozero__class_Ozero( X ), Y ) =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.92/1.56 ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.56 T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.92/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.56 tc_Nat_Onat, T, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, Z ), X ) ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.56 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ), Z ), X ) }
% 0.92/1.56 .
% 0.92/1.56 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ), Z =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.92/1.56 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) }.
% 0.92/1.56 { ! Y = X, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.92/1.56 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), ! hAPP(
% 0.92/1.56 c_Polynomial_Ocoeff( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 0.92/1.56 , Y ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X, Z, Y ) =
% 0.92/1.56 c_Polynomial_OAbs__poly( X, c_Nat_Onat_Onat__case( X, Z,
% 0.92/1.56 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 0.92/1.56 { c_HOL_Obool_Obool__size( c_fFalse ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Nat_Onat ) }.
% 0.92/1.56 { c_HOL_Obool_Obool__size( c_fTrue ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Nat_Onat ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.92/1.56 X ) ) }.
% 0.92/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.92/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.92/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.92/1.56 Y ) }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.92/1.56 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.56 Y ), ! Z = Y }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.92/1.56 Z ), ! Z = Y }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.92/1.56 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.92/1.56 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.92/1.56 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.92/1.56 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.92/1.56 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.92/1.56 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.92/1.56 , ! Z = Y }.
% 0.92/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.56 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.56 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.92/1.56 , ! Z = Y }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.92/1.56 , ! Y = Z }.
% 0.92/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.56 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.92/1.56 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.56 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.92/1.56 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.92/1.56 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.92/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.92/1.56 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.92/1.56 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.92/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.56 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.92/1.56 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.92/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.56 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.92/1.56 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.92/1.56 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.92/1.56 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.92/1.56 { alpha63( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.92/1.56 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.92/1.56 { alpha63( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.92/1.56 ( X, Y ), Z ) ) }.
% 0.92/1.56 { ! alpha63( X, Y, Z ), alpha65( X, Y, Z ), Z = Y }.
% 0.92/1.56 { ! alpha63( X, Y, Z ), alpha65( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.92/1.56 ) ) }.
% 0.92/1.56 { ! alpha65( X, Y, Z ), alpha63( X, Y, Z ) }.
% 0.92/1.56 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha63( X, Y, Z ) }.
% 0.92/1.56 { ! alpha65( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.92/1.56 }.
% 0.92/1.56 { ! alpha65( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.92/1.56 X, Y ), Z ) ), alpha65( X, Y, Z ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.92/1.56 X, Y, Z ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.56 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.92/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.56 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.92/1.56 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.92/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.56 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.56 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.56 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.56 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.56 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.56 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.56 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.56 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.92/1.56 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.92/1.56 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.92/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.92/1.56 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.56 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.92/1.56 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.56 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.92/1.56 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.92/1.56 ( X, Z, Y ) }.
% 0.92/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.56 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.56 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.92/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.56 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.92/1.56 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.92/1.56 , ! Z = Y }.
% 0.92/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.56 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.56 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.56 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.92/1.56 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.92/1.56 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.92/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.56 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.92/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.92/1.56 ( X, T, Y ) }.
% 0.92/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.92/1.56 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.92/1.56 , Y, Z ) ) }.
% 0.92/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.92/1.56 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.92/1.56 ( X, Z, Y ) }.
% 0.92/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.92/1.56 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.92/1.56 , T, Y ) ) }.
% 0.92/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.92/1.56 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.92/1.56 , Y, T ) ) }.
% 0.92/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.92/1.56 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.92/1.56 , T, Y ) ) }.
% 0.92/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.56 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.92/1.56 , T ) ) }.
% 0.92/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.92/1.56 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.92/1.56 ( X, Z, Y ) }.
% 0.92/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.92/1.56 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.92/1.56 ( X, Z, Y ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.92/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Nat_Onat ), X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.56 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.92/1.56 .
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Nat_Onat ), X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.92/1.56 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.92/1.56 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.92/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.92/1.56 .
% 0.92/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.92/1.56 .
% 0.92/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.92/1.56 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.92/1.56 X ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.92/1.56 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.92/1.56 }.
% 0.92/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.92/1.56 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.92/1.56 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.92/1.56 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.92/1.56 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.92/1.56 .
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.92/1.56 .
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.92/1.56 .
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.92/1.56 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.92/1.56 , X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.92/1.56 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.56 ( tc_Nat_Onat ), X ), ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z
% 0.92/1.56 ) = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ), Z = Y }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.56 ( tc_Nat_Onat ), X ), ! Z = Y, c_Groups_Otimes__class_Otimes( tc_Nat_Onat
% 0.92/1.56 , X, Z ) = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) }.
% 0.92/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_OAbs__poly( X,
% 0.92/1.56 c_Polynomial_Ocoeff( X, Y ) ) = Y }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.56 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.92/1.56 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, T, Z ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.56 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.92/1.56 ( X, c_Groups_Otimes__class_Otimes( X, Y, T ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Z, T ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.92/1.56 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.92/1.56 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.92/1.56 ( X, c_Groups_Otimes__class_Otimes( X, Z, T ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.56 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.56 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.56 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.92/1.56 , c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.92/1.56 Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.56 ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.92/1.56 T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.56 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.92/1.56 ( X, c_Groups_Otimes__class_Otimes( X, Y, T ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Z, Y ) ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.92/1.56 .
% 0.92/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Z, Y ) ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.92/1.56 .
% 0.92/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.56 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.56 , c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z,
% 0.92/1.56 Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.56 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.56 , c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.92/1.56 Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.56 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.92/1.56 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.56 ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.92/1.56 T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.56 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.92/1.56 ( X, c_Groups_Otimes__class_Otimes( X, Y, T ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.92/1.56 ), c_Groups_Otimes__class_Otimes( X, T, Y ) ), alpha5( X, Y, Z, T ),
% 0.92/1.56 alpha30( X, Y, Z, T ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z, T ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.92/1.56 ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha30( X, Y, Z, T ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.92/1.56 ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.92/1.56 { ! alpha30( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.56 { ! alpha30( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.56 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha30( X, Y, Z, T ) }.
% 0.92/1.56 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.92/1.56 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.92/1.56 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha5( X, Y, Z, T ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.92/1.56 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ), alpha6( X, Y, Z, T ),
% 0.92/1.56 alpha31( X, Y, Z, T ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z, T ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.92/1.56 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha31( X, Y, Z, T ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.92/1.56 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.92/1.56 { ! alpha31( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.56 { ! alpha31( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.56 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha31( X, Y, Z, T ) }.
% 0.92/1.56 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.92/1.56 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.92/1.56 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha6( X, Y, Z, T ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.56 , c_Groups_Otimes__class_Otimes( X, Y, Y ), c_Groups_Ozero__class_Ozero(
% 0.92/1.56 X ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.92/1.56 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.92/1.56 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.92/1.56 ) ) }.
% 0.92/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.56 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.92/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.92/1.56 ) ) }.
% 0.92/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.56 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.56 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.92/1.56 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.56 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.92/1.56 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.92/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.92/1.56 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.92/1.56 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.92/1.56 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.92/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.92/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.92/1.56 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.92/1.56 , Y, T ) ) }.
% 0.92/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.92/1.56 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha7( X, Y ) }.
% 0.92/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.92/1.56 { ! alpha7( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.92/1.56 c_Nat_OSuc( X ) ) }.
% 0.92/1.56 { ! alpha7( X, Y ), Y = c_Nat_OSuc( skol11( Z, Y ) ) }.
% 0.92/1.56 { ! alpha7( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol11( X,
% 0.92/1.56 Y ), X ) }.
% 0.92/1.56 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.92/1.56 ), alpha7( X, Y ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.56 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol12( X ) ) }.
% 0.92/1.56 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.92/1.56 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.56 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.56 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.56 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.92/1.56 tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol13( X, Y ) ) ) }.
% 0.92/1.56 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.92/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.92/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.92/1.56 .
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, Z ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ) ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.56 tc_Nat_Onat ), Y ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.92/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ),
% 0.92/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.92/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.56 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.92/1.56 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Nat_Onat ), Z ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.57 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.92/1.57 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.57 ( tc_Nat_Onat ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Nat_Onat ), Y ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.57 ( tc_Nat_Onat ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Nat_Onat ), X ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.57 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Nat_Onat ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Otimes__class_Otimes
% 0.92/1.57 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, c_Nat_OSuc( Z ), X ) ) }.
% 0.92/1.57 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.92/1.57 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.92/1.57 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 0.92/1.57 .
% 0.92/1.57 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.92/1.57 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.92/1.57 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.92/1.57 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, T
% 0.92/1.57 , Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, T
% 0.92/1.57 , Z ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.92/1.57 ), c_Groups_Otimes__class_Otimes( X, T, Y ) ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.92/1.57 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, T, Y ) ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.92/1.57 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.92/1.57 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.92/1.57 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Y, Z ) ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.92/1.57 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.92/1.57 ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.92/1.57 , U ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.92/1.57 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , U ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X
% 0.92/1.57 , Z, U ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.92/1.57 ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.92/1.57 , U ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.92/1.57 ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.92/1.57 , U ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.57 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.92/1.57 , Y, T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.57 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Y
% 0.92/1.57 , T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.57 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.92/1.57 , Y, T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.57 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Y
% 0.92/1.57 , T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.92/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.92/1.57 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.92/1.57 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.57 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.92/1.57 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.92/1.57 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.57 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.92/1.57 ) ) }.
% 0.92/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.57 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.92/1.57 ) ) }.
% 0.92/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.57 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.92/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.57 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z )
% 0.92/1.57 , c_Groups_Otimes__class_Otimes( X, Y, Y ) ) ), ! Z =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 }.
% 0.92/1.57 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.92/1.57 X, Y, Y ) ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.92/1.57 X, Y, Y ) ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.57 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z
% 0.92/1.57 ), c_Groups_Otimes__class_Otimes( X, Y, Y ) ),
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.92/1.57 ) }.
% 0.92/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.92/1.57 ) }.
% 0.92/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.92/1.57 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.57 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 0.92/1.57 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.92/1.57 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ), Z, T ), Y ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.92/1.57 , alpha47( X, Y, Z, T ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Polynomial_Opoly( X ), c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Polynomial_Opoly( X ), Z, T ), Y ), ! alpha47( X, Y, Z, T ),
% 0.92/1.57 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 0.92/1.57 { ! alpha47( X, Y, Z, T ), alpha8( X, Z, T ) }.
% 0.92/1.57 { ! alpha47( X, Y, Z, T ), alpha32( X, Y, T ) }.
% 0.92/1.57 { ! alpha8( X, Z, T ), ! alpha32( X, Y, T ), alpha47( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha32( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), alpha48( X, Y, Z ) }.
% 0.92/1.57 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha32( X
% 0.92/1.57 , Y, Z ) }.
% 0.92/1.57 { ! alpha48( X, Y, Z ), alpha32( X, Y, Z ) }.
% 0.92/1.57 { ! alpha48( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.57 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 0.92/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha48( X
% 0.92/1.57 , Y, Z ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 0.92/1.57 ), c_Polynomial_Odegree( X, Z ) ), alpha48( X, Y, Z ) }.
% 0.92/1.57 { ! alpha8( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.57 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha8( X, Y
% 0.92/1.57 , Z ) }.
% 0.92/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha8( X
% 0.92/1.57 , Y, Z ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.92/1.57 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.57 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.92/1.57 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.92/1.57 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ), alpha9
% 0.92/1.57 ( X, Y, Z ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.92/1.57 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! alpha9( X, Y, Z ),
% 0.92/1.57 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.92/1.57 { ! alpha9( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 0.92/1.57 ( X ) ) }.
% 0.92/1.57 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.92/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.92/1.57 alpha9( X, Y, Z ) }.
% 0.92/1.57 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.92/1.57 , skol14( T, U, Z ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Polynomial_Odegree( X, Y ), Z ) }.
% 0.92/1.57 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ), skol14( X
% 0.92/1.57 , Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.92/1.57 Y ), Z ) }.
% 0.92/1.57 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.57 Z, c_Polynomial_Odegree( X, Y ) ), c_Orderings_Oord__class_Oless(
% 0.92/1.57 tc_Nat_Onat, Z, skol15( T, U, Z ) ) }.
% 0.92/1.57 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.57 Z, c_Polynomial_Odegree( X, Y ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.92/1.57 skol15( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.92/1.57 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.92/1.57 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.92/1.57 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.92/1.57 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 0.92/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.92/1.57 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.92/1.57 .
% 0.92/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.92/1.57 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.92/1.57 }.
% 0.92/1.57 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.92/1.57 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.92/1.57 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 0.92/1.57 .
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.92/1.57 , c_Polynomial_Opdivmod__rel( X, c_Polynomial_Osmult( X, W, U ), T,
% 0.92/1.57 c_Polynomial_Osmult( X, W, Z ), c_Polynomial_Osmult( X, W, Y ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.92/1.57 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.92/1.57 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.92/1.57 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 0.92/1.57 c_Polynomial_Opdivmod__rel( X, U, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Polynomial_Opoly( X ), T, V1 ), V0, c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Polynomial_Opoly( X ), c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Polynomial_Opoly( X ), T, W ), Y ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.92/1.57 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.92/1.57 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, U, Z ), c_Groups_Otimes__class_Otimes(
% 0.92/1.57 X, W, T ) ), Y ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, U ), T ),
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, X, U ), Z ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, T
% 0.92/1.57 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes
% 0.92/1.57 ( tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z
% 0.92/1.57 ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z )
% 0.92/1.57 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, Y, U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), Z ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), T ),
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, Y, U ), Z ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.92/1.57 , Z ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T ), Z ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), T ),
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, Y, U ), Z ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.92/1.57 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.57 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.92/1.57 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, U, Z )
% 0.92/1.57 , c_Groups_Otimes__class_Otimes( X, W, T ) ), Y ) }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.92/1.57 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.92/1.57 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.92/1.57 ) }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.92/1.57 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.92/1.57 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.92/1.57 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.92/1.57 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.92/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.92/1.57 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ) ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.92/1.57 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.92/1.57 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.92/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Ominus__class_Ominus( X, Z
% 0.92/1.57 , Y ) ) = c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes
% 0.92/1.57 ( X, T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.92/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Ominus__class_Ominus( X, Z
% 0.92/1.57 , Y ) ) = c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes
% 0.92/1.57 ( X, T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.92/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, T, Z
% 0.92/1.57 ), Y ) = c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes
% 0.92/1.57 ( X, T, Y ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, T, Z
% 0.92/1.57 ), Y ) = c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes
% 0.92/1.57 ( X, T, Y ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.92/1.57 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.92/1.57 c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.57 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.92/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.92/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 Y, c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.92/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.92/1.57 { ! class_Groups_Ocomm__monoid__mult( X ), c_Groups_Otimes__class_Otimes( X
% 0.92/1.57 , Y, c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.92/1.57 { ! class_Groups_Omonoid__mult( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.92/1.57 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.92/1.57 { ! class_Groups_Ocomm__monoid__mult( X ), c_Groups_Otimes__class_Otimes( X
% 0.92/1.57 , c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.92/1.57 { ! class_Groups_Omonoid__mult( X ), c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.92/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.92/1.57 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.92/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.92/1.57 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.92/1.57 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.92/1.57 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.92/1.57 ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.92/1.57 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.92/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.92/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.92/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.92/1.57 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.92/1.57 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.92/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.92/1.57 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.92/1.57 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.92/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.92/1.57 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.92/1.57 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.57 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes
% 0.92/1.57 ( tc_Nat_Onat, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X )
% 0.92/1.57 ) }.
% 0.92/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.92/1.57 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 0.92/1.57 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 0.92/1.57 tc_Nat_Onat ) ) }.
% 0.92/1.57 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.92/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.92/1.57 tc_Nat_Onat ) }.
% 0.92/1.57 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.92/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.92/1.57 tc_Nat_Onat ) }.
% 0.92/1.57 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.92/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, Y, X ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.92/1.57 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, c_Groups_Oone__class_Oone
% 0.92/1.57 ( tc_Nat_Onat ) ) = X }.
% 0.92/1.57 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) =
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ), Y =
% 0.92/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.92/1.57 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) =
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ), X =
% 0.92/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.92/1.57 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.92/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.92/1.57 tc_Nat_Onat ) = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) }.
% 0.92/1.57 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.92/1.57 tc_Nat_Onat ), X ) = X }.
% 0.92/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 0.92/1.57 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.92/1.57 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.92/1.57 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.92/1.57 c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.92/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.92/1.57 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 0.92/1.57 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.92/1.57 c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.57 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.92/1.57 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.92/1.57 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.92/1.57 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.92/1.57 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.92/1.57 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 0.92/1.57 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.92/1.57 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.92/1.57 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.92/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.92/1.57 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 0.92/1.57 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.92/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.92/1.57 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.92/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.92/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.92/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.92/1.57 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.57 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.92/1.57 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.57 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.92/1.57 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.92/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.92/1.57 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.92/1.57 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.92/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.57 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.92/1.57 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.92/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 0.92/1.57 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 0.92/1.57 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.57 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.92/1.57 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.92/1.57 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.92/1.57 ( X ) ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.92/1.57 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.92/1.57 , Z, Y ) }.
% 0.92/1.57 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, W, U ), T ) =
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.92/1.57 , Y ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ) = Y }.
% 0.92/1.57 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, W, Z
% 0.92/1.57 ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, W, U ), T ) =
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.92/1.57 , Y ) }.
% 0.92/1.57 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, W, U ), T ) =
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.92/1.57 , Y ), T = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes
% 0.92/1.57 ( X, c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) }.
% 0.92/1.57 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, Z, W
% 0.92/1.57 ), U ), Y ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, W, U ), T ) =
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.92/1.57 , Y ) }.
% 0.92/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes( X, U, T
% 0.92/1.57 ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.92/1.57 ), c_Groups_Ominus__class_Ominus( X, T, Y ) ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.92/1.57 ), Y ) ), c_Groups_Otimes__class_Otimes( X, Z,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__semidom( X ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Groups_Oone__class_Oone( X ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__semidom( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.92/1.57 .
% 0.92/1.57 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.92/1.57 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Oone__class_Oone( X ), c_Groups_Otimes__class_Otimes( X, Y, Z
% 0.92/1.57 ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.92/1.57 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.92/1.57 ) }.
% 0.92/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Z, Y ), Y ) =
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.92/1.57 c_Groups_Oone__class_Oone( X ) ), Y ) }.
% 0.92/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.92/1.57 , c_Groups_Otimes__class_Otimes( X, Y, Z ) ) =
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.92/1.57 c_Groups_Oone__class_Oone( X ) ), Z ) }.
% 0.92/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.92/1.57 , Y ) = c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X
% 0.92/1.57 , c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ), Y ) }
% 0.92/1.57 .
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.57 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.92/1.57 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.92/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.92/1.57 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.92/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.57 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.92/1.57 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.92/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Nat_Onat, Z, X ), Y ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.92/1.57 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.92/1.57 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.92/1.57 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.92/1.57 ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.92/1.57 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.92/1.57 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.92/1.57 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.92/1.57 ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.92/1.57 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.92/1.57 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Nat_Onat, Z, X ), Y ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Nat_Onat, Z, Y ), X ) }.
% 0.92/1.57 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.92/1.57 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.92/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.92/1.57 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.92/1.57 { ! Y = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ), X =
% 0.92/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Ozero__class_Ozero
% 0.92/1.57 ( tc_Nat_Onat ) }.
% 0.92/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 0.92/1.57 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.57 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W, U
% 0.92/1.57 ), T ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.92/1.57 , Z, U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ), Y ) }.
% 0.92/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.57 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ), Y ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, W, U ), T ),
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.92/1.57 , Y ) ) }.
% 0.92/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.57 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W, U
% 0.92/1.57 ), T ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.92/1.57 , Z, U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) ) }.
% 0.92/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.57 , T, c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, W, U ), T ),
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.92/1.57 , Y ) ) }.
% 0.92/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W, U )
% 0.92/1.57 , T ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 Z, U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ), Y ) }.
% 0.92/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ), Y ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, W, U ), T ),
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.92/1.57 , Y ) ) }.
% 0.92/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W, U )
% 0.92/1.57 , T ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 Z, U ), Y ) ), c_Orderings_Oord__class_Oless( X, T,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) ) }.
% 0.92/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.92/1.57 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, W, U ), T ),
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.92/1.57 , Y ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.92/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.92/1.57 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.92/1.57 ( X ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Z, Y ), Y ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.92/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.92/1.57 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.92/1.57 ( X ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Y, Z ), Y ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.92/1.57 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.57 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.57 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.92/1.57 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.92/1.57 ) ) = X }.
% 0.92/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.92/1.57 , ! alpha10( X, Y, Z ) }.
% 0.92/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.92/1.57 , ! alpha33( X, Y, Z ) }.
% 0.92/1.57 { alpha10( X, Y, Z ), alpha33( X, Y, Z ), hBOOL( hAPP( Z,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.92/1.57 { ! alpha33( X, Y, Z ), ! hBOOL( hAPP( Z, skol16( T, U, Z ) ) ) }.
% 0.92/1.57 { ! alpha33( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.92/1.57 skol16( X, Y, Z ) ) }.
% 0.92/1.57 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.92/1.57 ) ), alpha33( X, Y, Z ) }.
% 0.92/1.57 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.92/1.57 }.
% 0.92/1.57 { ! alpha10( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Nat_Onat ) ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha10( X, Y, Z ) }.
% 0.92/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.92/1.57 , alpha11( X, Y, Z ) }.
% 0.92/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.92/1.57 , alpha34( X, Y, Z ) }.
% 0.92/1.57 { ! alpha11( X, Y, Z ), ! alpha34( X, Y, Z ), hBOOL( hAPP( Z,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.92/1.57 { ! alpha34( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.92/1.57 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.92/1.57 { ! hBOOL( hAPP( Z, skol17( T, U, Z ) ) ), alpha34( X, Y, Z ) }.
% 0.92/1.57 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol17( X, Y, Z ) ),
% 0.92/1.57 alpha34( X, Y, Z ) }.
% 0.92/1.57 { ! alpha11( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.92/1.57 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.92/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha11( X, Y, Z ) }
% 0.92/1.57 .
% 0.92/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha11
% 0.92/1.57 ( X, Y, Z ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, X, U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, U ), Z ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.92/1.57 , Z ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.92/1.57 , Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, X, U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, U ), Z ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), T ),
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, Y, U ), Z ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.92/1.57 , Z ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, X, U ), T ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, U ), Z ),
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.92/1.57 = Z }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.92/1.57 = Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), T ) =
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, Y, U ), Z ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, Y, U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), Z ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z )
% 0.92/1.57 ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z )
% 0.92/1.57 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, Y, U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), Z ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, U ), T ),
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, X, U ), Z ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.92/1.57 T, c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.92/1.57 ( tc_Nat_Onat, X, Y ), U ), Z ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, Y, U ), T ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), Z ), T =
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z )
% 0.92/1.57 }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z )
% 0.92/1.57 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes
% 0.92/1.57 ( tc_Nat_Onat, Y, U ), T ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), Z ) }.
% 0.92/1.57 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Y, Y ), c_Groups_Oone__class_Oone( X )
% 0.92/1.57 ) = c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.92/1.57 , c_Groups_Oone__class_Oone( X ) ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.92/1.57 c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.92/1.57 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.92/1.57 X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, U, c_Groups_Ominus__class_Ominus( X, T
% 0.92/1.57 , Y ) ), c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus
% 0.92/1.57 ( X, U, Z ), Y ) ) }.
% 0.92/1.57 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Polynomial_Opoly( X ), c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.92/1.57 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z ) )
% 0.92/1.57 , c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.92/1.57 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.92/1.57 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.92/1.57 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.92/1.57 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.92/1.57 ( X, Y ), Z ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.92/1.57 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.92/1.57 ( X, Z ), Y ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.57 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.57 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.92/1.57 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.92/1.57 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.92/1.57 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.92/1.57 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.92/1.57 tc_Polynomial_Opoly( X ), Y ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.92/1.57 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.92/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.92/1.57 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.92/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.92/1.57 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.92/1.57 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.92/1.57 ) }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 0.92/1.57 ) ) }.
% 0.92/1.57 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.92/1.57 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.92/1.57 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.92/1.57 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.92/1.57 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.92/1.57 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.92/1.57 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.92/1.57 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.92/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.92/1.57 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.92/1.57 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.92/1.57 ( X, Z ) }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.92/1.57 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.92/1.57 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.92/1.57 c_Polynomial_Odegree( X, Y ) }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.92/1.57 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.92/1.57 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.92/1.57 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.92/1.57 Y ) ) = Y }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 Z, Y ) ) = Y }.
% 0.92/1.57 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.57 Y ) ) }.
% 0.92/1.57 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.92/1.57 , Y ) }.
% 0.92/1.57 { ! class_Rings_Oring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.57 Y ) ) }.
% 0.92/1.57 { ! class_Rings_Oring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.92/1.57 ( X, Y ) ) = c_Groups_Otimes__class_Otimes( X, Z, Y ) }.
% 0.92/1.57 { ! class_Rings_Oidom( X ), ! c_Groups_Otimes__class_Otimes( X, Z, Z ) =
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Y, Y ), Z = Y, Z =
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.92/1.57 { ! class_Rings_Oidom( X ), ! Z = Y, c_Groups_Otimes__class_Otimes( X, Z, Z
% 0.92/1.57 ) = c_Groups_Otimes__class_Otimes( X, Y, Y ) }.
% 0.92/1.57 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Z, Z ) = c_Groups_Otimes__class_Otimes
% 0.92/1.57 ( X, Y, Y ) }.
% 0.92/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.92/1.57 , Y ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Otimes__class_Otimes
% 0.92/1.57 ( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.92/1.57 , Y ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Otimes__class_Otimes
% 0.92/1.57 ( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.57 Y ) ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Otimes__class_Otimes
% 0.92/1.57 ( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.57 Y ) ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Otimes__class_Otimes
% 0.92/1.57 ( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.92/1.57 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.92/1.57 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.92/1.57 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.92/1.57 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.92/1.57 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.92/1.57 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.92/1.57 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 = Y }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.92/1.57 ) }.
% 0.92/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.92/1.57 ( X ) }.
% 0.92/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.92/1.57 , Y ) }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.92/1.57 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.92/1.57 ) }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.92/1.57 ) }.
% 0.92/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.92/1.57 = Y }.
% 0.92/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.92/1.57 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.57 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.92/1.57 ( X, Y ), Y ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.92/1.57 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.57 ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.57 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.92/1.57 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.92/1.57 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.92/1.57 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.57 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.92/1.57 .
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.57 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.92/1.57 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.92/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.92/1.57 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , Y ) }.
% 0.92/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.92/1.57 , Y ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.92/1.57 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.92/1.57 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 X ) }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.92/1.57 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.92/1.57 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.92/1.57 ( X, Y ) }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.92/1.57 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.57 Z ) = Y }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.92/1.57 X, Y ) }.
% 0.92/1.57 { ! class_Rings_Oring__1__no__zero__divisors( X ), !
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.92/1.57 , Y = c_Groups_Oone__class_Oone( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.92/1.57 ( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.92/1.57 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.92/1.57 c_Groups_Oone__class_Oone( X ), c_Groups_Otimes__class_Otimes( X, Y, Y )
% 0.92/1.57 = c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.57 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.92/1.57 }.
% 0.92/1.57 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.92/1.57 ) = c_Groups_Otimes__class_Otimes( X, c_Groups_Ouminus__class_Ouminus( X
% 0.92/1.57 , c_Groups_Oone__class_Oone( X ) ), Y ) }.
% 0.92/1.57 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.92/1.57 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.92/1.57 X, Y ) ) }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.92/1.57 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.92/1.57 , Y ) ) }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.92/1.57 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.92/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.92/1.57 X, Z, Y ) }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.92/1.57 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.92/1.57 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 0.92/1.57 }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.92/1.57 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.92/1.57 T ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Polynomial_Odegree( X, c_Groups_Ominus__class_Ominus(
% 0.92/1.57 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.92/1.57 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.92/1.57 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.92/1.57 , T = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! V0 =
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 0.92/1.57 c_Polynomial_OpCons( X, W, Y ) ), c_Polynomial_Odegree( X, T ) ), hAPP(
% 0.92/1.57 c_Polynomial_Ocoeff( X, T ), c_Polynomial_Odegree( X, T ) ) ),
% 0.92/1.57 c_Polynomial_Opdivmod__rel( X, c_Polynomial_OpCons( X, W, U ), T,
% 0.92/1.57 c_Polynomial_OpCons( X, V0, Z ), c_Groups_Ominus__class_Ominus(
% 0.92/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, W, Y ),
% 0.92/1.57 c_Polynomial_Osmult( X, V0, T ) ) ) }.
% 0.92/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.92/1.57 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.92/1.57 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.92/1.57 { ! class_RealVector_Oreal__normed__field( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.92/1.57 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 0.92/1.57 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.92/1.57 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.92/1.57 ), Y ) }.
% 0.92/1.57 { ! class_RealVector_Oreal__normed__field( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.92/1.57 ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_RealVector_Oreal__normed__field( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.92/1.57 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 }.
% 0.92/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.57 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), c_Groups_Otimes__class_Otimes( X, T,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Otimes__class_Otimes( X, T,
% 0.92/1.57 Z ), Y ) }.
% 0.92/1.57 { ! class_RealVector_Oreal__normed__field( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 0.92/1.57 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 0.92/1.57 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.92/1.57 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , ! c_Groups_Otimes__class_Otimes( X, T, Y ) = Z, T =
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , ! T = c_Groups_Otimes__class_Otimes( X, Z, Y ),
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T =
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Z, Y ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , ! T = c_Groups_Otimes__class_Otimes( X, Z, Y ),
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, T, Y ) = Z }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , ! c_Groups_Otimes__class_Otimes( X, T, Y ) = Z, T =
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.92/1.57 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.92/1.57 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 0.92/1.57 ( X ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.92/1.57 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.92/1.57 c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.57 , Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X
% 0.92/1.57 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.92/1.57 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 0.92/1.57 , c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes( X, W,
% 0.92/1.57 U ), c_Groups_Otimes__class_Otimes( X, T, Z ) ), Y ) =
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.92/1.57 Z ), Y ) ), c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, W,
% 0.92/1.57 T ), Y ), Z ) ) }.
% 0.92/1.57 { ! class_Lattices_Oab__semigroup__idem__mult( X ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Z, c_Groups_Otimes__class_Otimes( X, Z
% 0.92/1.57 , Y ) ) = c_Groups_Otimes__class_Otimes( X, Z, Y ) }.
% 0.92/1.57 { ! class_Lattices_Oab__semigroup__idem__mult( X ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Y, Y ) = Y }.
% 0.92/1.57 { ! class_Lattices_Oab__semigroup__idem__mult( X ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Y, Y ) = Y }.
% 0.92/1.57 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.92/1.57 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.92/1.57 hAPP( Z, Y ) ) }.
% 0.92/1.57 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.92/1.57 ( X, Y ), Z = Y }.
% 0.92/1.57 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.92/1.57 ( X, Y ) }.
% 0.92/1.57 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.92/1.57 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.92/1.57 ) ) }.
% 0.92/1.57 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.92/1.57 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.92/1.57 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.92/1.57 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.92/1.57 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.92/1.57 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , c_Groups_Otimes__class_Otimes( X, Z, Y ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.57 , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.92/1.57 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.57 , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.57 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Z, Y ), T ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.92/1.57 , Y ), T ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) }.
% 0.92/1.57 { ! class_Fields_Ofield__inverse__zero( X ), c_Groups_Otimes__class_Otimes
% 0.92/1.57 ( X, c_Rings_Oinverse__class_Odivide( X, U, T ),
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Otimes__class_Otimes( X, U,
% 0.92/1.57 Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.92/1.57 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.92/1.57 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.92/1.57 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.92/1.57 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.92/1.57 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.92/1.57 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.57 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha12( X, Y, Z ), alpha35
% 0.92/1.57 ( X, Y, Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha12( X, Y, Z
% 0.92/1.57 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.92/1.57 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha35( X, Y, Z
% 0.92/1.57 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.92/1.57 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.92/1.57 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.92/1.57 ( X ), Y ), alpha35( X, Y, Z ) }.
% 0.92/1.57 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.92/1.57 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ), alpha12( X, Y, Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha13( X, Y, Z ), alpha36
% 0.92/1.57 ( X, Y, Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha13( X, Y, Z
% 0.92/1.57 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.92/1.57 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha36( X, Y, Z
% 0.92/1.57 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.92/1.57 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.92/1.57 { ! alpha36( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! alpha36( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.92/1.57 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ), alpha36( X, Y, Z ) }.
% 0.92/1.57 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.92/1.57 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Y ), alpha13( X, Y, Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha14( X, Y, Z ), alpha37
% 0.92/1.57 ( X, Y, Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha14( X, Y, Z
% 0.92/1.57 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha37( X, Y, Z
% 0.92/1.57 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.92/1.57 { ! alpha37( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! alpha37( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.57 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 ), alpha37( X, Y, Z ) }.
% 0.92/1.57 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.92/1.57 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.92/1.57 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.57 ), alpha14( X, Y, Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 0.92/1.57 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha15( X, Y, Z ), alpha38( X,
% 0.92/1.57 Y, Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha15( X, Y, Z
% 0.92/1.57 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.57 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha38( X, Y, Z
% 0.92/1.57 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.57 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! alpha38( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! alpha38( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.57 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.57 ), alpha38( X, Y, Z ) }.
% 0.92/1.57 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.92/1.57 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.92/1.57 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 ), alpha15( X, Y, Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.92/1.57 , Y, Z ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.92/1.57 , Y, Z ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 0.92/1.57 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, U, Z ) = c_Groups_Otimes__class_Otimes
% 0.92/1.57 ( X, T, Y ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), ! c_Groups_Otimes__class_Otimes( X, U,
% 0.92/1.57 Z ) = c_Groups_Otimes__class_Otimes( X, T, Y ),
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.92/1.57 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Y, T ), c_Groups_Otimes__class_Otimes(
% 0.92/1.57 X, Y, Z ) ) = c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.92/1.57 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, T, Y ), c_Groups_Otimes__class_Otimes(
% 0.92/1.57 X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.92/1.57 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha39( X, Y, Z, T ) }.
% 0.92/1.57 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha16( X, Y, Z ) }.
% 0.92/1.57 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha39( X, Y, Z, T ), !
% 0.92/1.57 alpha16( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 0.92/1.57 { ! alpha39( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T =
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Y, Z ) }.
% 0.92/1.57 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha39( X, Y, Z, T ) }.
% 0.92/1.57 { ! T = c_Groups_Otimes__class_Otimes( X, Y, Z ), alpha39( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha16( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { Z = c_Groups_Ozero__class_Ozero( X ), alpha16( X, Y, Z ) }.
% 0.92/1.57 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha16( X, Y, Z ) }.
% 0.92/1.57 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha40( X, Y, Z, T ) }.
% 0.92/1.57 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha17( X, Y, T ) }.
% 0.92/1.57 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha40( X, Y, Z, T ), !
% 0.92/1.57 alpha17( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.92/1.57 { ! alpha40( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, T, Y ) = Z }.
% 0.92/1.57 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha40( X, Y, Z, T ) }.
% 0.92/1.57 { ! c_Groups_Otimes__class_Otimes( X, T, Y ) = Z, alpha40( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha17( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { Y = c_Groups_Ozero__class_Ozero( X ), alpha17( X, Y, Z ) }.
% 0.92/1.57 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha17( X, Y, Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.92/1.57 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.57 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.92/1.57 X ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.57 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.92/1.57 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.57 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.57 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.92/1.57 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 0.92/1.57 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.92/1.57 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.57 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.92/1.57 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.92/1.57 X ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.57 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.92/1.57 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.57 Z, Y ) ), alpha41( X, Y, Z, T ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.57 Z, Y ) ), alpha49( X, Y, Z, T ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha41( X, Y, Z
% 0.92/1.57 , T ), ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.92/1.57 { ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Y ), alpha54( X, Y, Z, T ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.92/1.57 , alpha49( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha54( X, Y, Z, T ), alpha49( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha54( X, Y, Z, T ), alpha59( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha54( X, Y, Z, T ), alpha18( X, Y, T ) }.
% 0.92/1.57 { ! alpha59( X, Y, Z, T ), ! alpha18( X, Y, T ), alpha54( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha59( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.92/1.57 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.57 alpha59( X, Y, Z, T ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 T, Y ) ), alpha59( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha41( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, T, Y ), Z ) }.
% 0.92/1.57 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.57 alpha41( X, Y, Z, T ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T,
% 0.92/1.57 Y ), Z ), alpha41( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.57 , alpha18( X, Y, Z ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.57 , alpha18( X, Y, Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.92/1.57 Z ), Y ), alpha42( X, Y, Z, T ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.92/1.57 Z ), Y ), alpha50( X, Y, Z, T ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha42( X, Y, Z
% 0.92/1.57 , T ), ! alpha50( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.92/1.57 { ! alpha50( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Z ), alpha55( X, Y, Z, T ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.92/1.57 , alpha50( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha55( X, Y, Z, T ), alpha50( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha55( X, Y, Z, T ), alpha60( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha55( X, Y, Z, T ), alpha19( X, Y, Z ) }.
% 0.92/1.57 { ! alpha60( X, Y, Z, T ), ! alpha19( X, Y, Z ), alpha55( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha60( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Y, Z ), T ) }.
% 0.92/1.57 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.57 alpha60( X, Y, Z, T ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.92/1.57 Z ), T ), alpha60( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha42( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 T, c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.92/1.57 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.92/1.57 alpha42( X, Y, Z, T ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 Y, Z ) ), alpha42( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.57 , alpha19( X, Y, Z ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.92/1.57 , alpha19( X, Y, Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Y
% 0.92/1.57 ), Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ), Z ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.57 Z, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, T, c_Groups_Otimes__class_Otimes( X, Z
% 0.92/1.57 , Y ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, T, c_Groups_Otimes__class_Otimes( X, Z, Y ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.92/1.57 Y ), Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, T, c_Groups_Otimes__class_Otimes( X, Z, Y ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.92/1.57 Y ), Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ), Z ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.57 Z, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Otimes__class_Otimes( X, T
% 0.92/1.57 , Y ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, Z, c_Groups_Otimes__class_Otimes( X, T, Y ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.57 Z, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.92/1.57 ), T ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, c_Groups_Otimes__class_Otimes( X, Z, Y ), T ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.92/1.57 Y ), Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.57 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.92/1.57 Z ) ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide
% 0.92/1.57 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.92/1.57 ) ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide(
% 0.92/1.57 X, T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, T, Y ) ), Y ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 0.92/1.57 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.92/1.57 ( X, c_Groups_Otimes__class_Otimes( X, Y, T ), Z ), Y ) }.
% 0.92/1.57 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Z, Y ) ), Y ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 0.92/1.57 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.92/1.57 ( X, T, c_Groups_Otimes__class_Otimes( X, Y, Z ) ), Y ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, U, Z ), c_Groups_Otimes__class_Otimes(
% 0.92/1.57 X, T, Y ) ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.57 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes( X, Y, T
% 0.92/1.57 ), Z ), Y ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.92/1.57 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, T, c_Groups_Otimes__class_Otimes( X, Y
% 0.92/1.57 , Z ) ), Y ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, U, Z ), c_Groups_Otimes__class_Otimes(
% 0.92/1.57 X, T, Y ) ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.92/1.57 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.92/1.57 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.92/1.57 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.92/1.57 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.92/1.57 ( X, Z, Y ) ), alpha43( X, Y, Z, T ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.92/1.57 ( X, Z, Y ) ), alpha51( X, Y, Z, T ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha43( X, Y, Z
% 0.92/1.57 , T ), ! alpha51( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.92/1.57 { ! alpha51( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Y ), alpha56( X, Y, Z, T ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.92/1.57 , alpha51( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha56( X, Y, Z, T ), alpha51( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha56( X, Y, Z, T ), alpha61( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha56( X, Y, Z, T ), alpha20( X, Y, T ) }.
% 0.92/1.57 { ! alpha61( X, Y, Z, T ), ! alpha20( X, Y, T ), alpha56( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha61( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.57 , Z, c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.92/1.57 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.57 alpha61( X, Y, Z, T ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Otimes__class_Otimes
% 0.92/1.57 ( X, T, Y ) ), alpha61( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha43( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.92/1.57 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ), Z ) }.
% 0.92/1.57 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.57 alpha43( X, Y, Z, T ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.92/1.57 , T, Y ), Z ), alpha43( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.57 , Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.57 , alpha20( X, Y, Z ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.92/1.57 ) ), alpha20( X, Y, Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.57 , T, Z ), Y ), alpha44( X, Y, Z, T ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.57 , T, Z ), Y ), alpha52( X, Y, Z, T ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha44( X, Y, Z
% 0.92/1.57 , T ), ! alpha52( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.92/1.57 { ! alpha52( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Z ), alpha57( X, Y, Z, T ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.92/1.57 , alpha52( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha57( X, Y, Z, T ), alpha52( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha57( X, Y, Z, T ), alpha62( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha57( X, Y, Z, T ), alpha21( X, Y, Z ) }.
% 0.92/1.57 { ! alpha62( X, Y, Z, T ), ! alpha21( X, Y, Z ), alpha57( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha62( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.57 , c_Groups_Otimes__class_Otimes( X, Y, Z ), T ) }.
% 0.92/1.57 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.57 alpha62( X, Y, Z, T ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.92/1.57 , Y, Z ), T ), alpha62( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha44( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 0.92/1.57 ( X, T, c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.92/1.57 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.92/1.57 alpha44( X, Y, Z, T ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Otimes__class_Otimes
% 0.92/1.57 ( X, Y, Z ) ), alpha44( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.57 , c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.57 , alpha21( X, Y, Z ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , Y ), alpha21( X, Y, Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.92/1.57 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, T, Y ), Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, T
% 0.92/1.57 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.57 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Otimes__class_Otimes( X
% 0.92/1.57 , Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Otimes__class_Otimes( X
% 0.92/1.57 , Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, T
% 0.92/1.57 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.92/1.57 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Otimes__class_Otimes( X
% 0.92/1.57 , T, Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 0.92/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T, Z ), Y ) =
% 0.92/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.92/1.57 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 0.92/1.57 tc_Polynomial_Opoly( X ), Z, Y ) ), c_Polynomial_Osmult( X,
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 0.92/1.57 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 0.92/1.57 tc_Polynomial_Opoly( X ), Z, Y ) ) ), c_Polynomial_Odegree( X, Y ) ),
% 0.92/1.57 hAPP( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y )
% 0.92/1.57 ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 0.92/1.57 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.92/1.57 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 0.92/1.57 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.92/1.57 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.92/1.57 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 0.92/1.57 ( X ) ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.92/1.57 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.92/1.57 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.92/1.57 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.92/1.57 ( X ), Z, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.92/1.57 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.92/1.57 tc_Polynomial_Opoly( X ), Y ) ) = c_Divides_Odiv__class_Omod(
% 0.92/1.57 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.92/1.57 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.92/1.57 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.92/1.57 .
% 0.92/1.57 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.92/1.57 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.92/1.57 c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.92/1.57 , c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.92/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 0.92/1.57 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Omod(
% 0.92/1.57 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.92/1.57 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.92/1.57 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.92/1.57 ) }.
% 0.92/1.57 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.92/1.57 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.92/1.57 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 }.
% 0.92/1.57 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.92/1.57 c_Groups_Osgn__class_Osgn( X, c_Groups_Otimes__class_Otimes( X, Z, Y ) )
% 0.92/1.57 = c_Groups_Otimes__class_Otimes( X, c_Groups_Osgn__class_Osgn( X, Z ),
% 0.92/1.57 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, c_Groups_Osgn__class_Osgn( X, Z ),
% 0.92/1.57 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.92/1.57 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.92/1.57 .
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.92/1.57 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 0.92/1.57 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T,
% 0.92/1.57 c_Polynomial_Osmult( X, Y, Z ) ) = c_Divides_Odiv__class_Omod(
% 0.92/1.57 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.57 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.92/1.57 .
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.57 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.92/1.57 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.92/1.57 .
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.57 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.92/1.57 .
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.57 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.92/1.57 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.92/1.57 .
% 0.92/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 0.92/1.57 tc_Polynomial_Opoly( X ), Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.57 c_Polynomial_Odegree( X, c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.92/1.57 ( X ), Z, Y ) ), c_Polynomial_Odegree( X, Y ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.57 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.92/1.57 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.92/1.57 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.57 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.92/1.57 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.57 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.57 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.57 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.57 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.57 c_Groups_Oone__class_Oone( X ) ) }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.92/1.57 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.92/1.57 .
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.57 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.92/1.57 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.92/1.57 }.
% 0.92/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.57 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.92/1.57 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.92/1.57 }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, T, c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.92/1.57 ) ), Z ) = c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, T, c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.92/1.57 ) ), Y ) = c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 0.92/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.92/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.92/1.57 tc_Nat_Onat, Y, X ), X ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.92/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.92/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.92/1.57 tc_Nat_Onat, Y, X ), X ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) =
% 0.92/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.92/1.57 tc_Nat_Onat, X, Y ), Y ) }.
% 0.92/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.57 { ! c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.92/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.57 { c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.92/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.92/1.57 c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.57 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, skol18( X, Y ) ) }.
% 0.92/1.57 { ! Y = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ),
% 0.92/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.57 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ), X ), Y )
% 0.92/1.57 = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 0.92/1.57 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, c_Divides_Odiv__class_Omod
% 0.92/1.57 ( tc_Nat_Onat, Y, X ) ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.92/1.57 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Divides_Odiv__class_Omod(
% 0.92/1.57 tc_Nat_Onat, Z, Y ), X ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.92/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.92/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 0.92/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, Z, Y ), X ) ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat
% 0.92/1.57 , c_Nat_OSuc( X ), Y ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.57 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.57 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.92/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), Y ) }.
% 0.92/1.57 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.92/1.57 alpha22( X, Y, Z ) }.
% 0.92/1.57 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.92/1.57 alpha45( X, Y, Z ) }.
% 0.92/1.57 { ! alpha22( X, Y, Z ), ! alpha45( X, Y, Z ), hBOOL( hAPP( Z,
% 0.92/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ) }.
% 0.92/1.57 { ! alpha45( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.57 alpha53( X, Y, Z ) }.
% 0.92/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha45( X, Y, Z ) }.
% 0.92/1.57 { ! alpha53( X, Y, Z ), alpha45( X, Y, Z ) }.
% 0.92/1.57 { ! alpha53( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.92/1.57 ), alpha58( X, Y, Z, T ) }.
% 0.92/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol19( X, T, U ), X ),
% 0.92/1.57 alpha53( X, Y, Z ) }.
% 0.92/1.57 { ! alpha58( X, Y, Z, skol19( X, Y, Z ) ), alpha53( X, Y, Z ) }.
% 0.92/1.57 { ! alpha58( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), T ), hBOOL( hAPP( Z,
% 0.92/1.57 T ) ) }.
% 0.92/1.57 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, skol20( X, Y, T ) ), T ),
% 0.92/1.57 alpha58( X, Y, Z, T ) }.
% 0.92/1.57 { ! hBOOL( hAPP( Z, T ) ), alpha58( X, Y, Z, T ) }.
% 0.92/1.57 { ! alpha22( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.57 hBOOL( hAPP( Z, Y ) ) }.
% 0.92/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha22( X, Y, Z ) }.
% 0.92/1.57 { ! hBOOL( hAPP( Z, Y ) ), alpha22( X, Y, Z ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.92/1.57 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 tc_Nat_Onat, Y, c_Divides_Odiv__class_Omod( tc_Nat_Onat, T, X ) ), Z ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.92/1.57 tc_Nat_Onat ), X ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.92/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ), X ) =
% 0.92/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 0.92/1.57 X, Z, Y ) }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.92/1.57 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.92/1.57 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.92/1.57 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.92/1.57 c_Divides_Odiv__class_Omod( X, c_Groups_Otimes__class_Otimes( X, T, W ),
% 0.92/1.57 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Otimes__class_Otimes( X, Y
% 0.92/1.57 , U ), Z ) }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, c_Divides_Odiv__class_Omod( X, T, Z ),
% 0.92/1.57 Y ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Otimes__class_Otimes(
% 0.92/1.57 X, T, Y ), Z ) }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, T, Z ), c_Groups_Otimes__class_Otimes(
% 0.92/1.57 X, Y, Z ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Divides_Odiv__class_Omod( X, T, Y ), Z ) }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, T, Z ), c_Groups_Otimes__class_Otimes(
% 0.92/1.57 X, T, Y ) ) = c_Groups_Otimes__class_Otimes( X, T,
% 0.92/1.57 c_Divides_Odiv__class_Omod( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.92/1.57 c_Divides_Odiv__class_Omod( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 0.92/1.57 Y ) ), Y ) }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.92/1.57 c_Divides_Odiv__class_Omod( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.92/1.57 c_Divides_Odiv__class_Omod( X, c_Groups_Otimes__class_Otimes( X, T,
% 0.92/1.57 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.92/1.57 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.92/1.57 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.92/1.57 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 0.92/1.57 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 0.92/1.57 ), Z ) }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 0.92/1.57 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 T, Y ), Z ) }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.92/1.57 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 T, Z ), Y ) }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.92/1.57 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.92/1.57 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.92/1.57 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.92/1.57 ), Z ), Y ) }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.92/1.57 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 0.92/1.57 , Y ) ), Y ) }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.92/1.57 ( X, Y, Z ) }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 0.92/1.57 ( X, Z, Y ) }.
% 0.92/1.57 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.92/1.57 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 0.92/1.57 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.92/1.57 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 0.92/1.57 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 0.92/1.57 , U ), Z ) }.
% 0.92/1.57 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.92/1.57 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.92/1.57 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 0.92/1.57 Y ) ), Y ) }.
% 0.92/1.57 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.92/1.57 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.92/1.57 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 0.92/1.57 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.92/1.57 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.92/1.57 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.92/1.57 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.92/1.57 = c_Divides_Odiv__class_Omod( X, Y, Z ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, T ), Z ) = c_Divides_Odiv__class_Omod
% 0.92/1.57 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.92/1.57 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.92/1.57 ( X, c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Omod( X, Z
% 0.92/1.57 , Y ) ), Y ) }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Z, Y ), Z ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Z, Y ), Y ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.92/1.57 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.92/1.57 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.92/1.57 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.92/1.57 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.92/1.57 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.92/1.57 .
% 0.92/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.92/1.57 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.92/1.57 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.92/1.57 .
% 0.92/1.57 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.92/1.57 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol21( Z, Y
% 0.92/1.57 ), Y ) }.
% 0.92/1.57 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.92/1.57 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.92/1.57 skol21( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.92/1.57 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.92/1.57 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.92/1.57 , skol21( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 0.92/1.57 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.92/1.57 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.92/1.57 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.92/1.57 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.92/1.57 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.92/1.57 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.92/1.57 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 0.92/1.57 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 0.92/1.57 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.92/1.57 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 0.92/1.57 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.92/1.57 c_Polynomial_Opoly__gcd( X, Y, c_Divides_Odiv__class_Omod(
% 0.92/1.57 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 0.92/1.57 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 0.92/1.57 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 0.92/1.57 c_Polynomial_Opoly__gcd( X, Z, c_Divides_Odiv__class_Omod(
% 0.92/1.57 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 skol22( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, skol22( X, T, U ),
% 0.92/1.57 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.57 , Y ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 skol22( X, Y, Z ), Z ), Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y )
% 0.92/1.57 }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.92/1.57 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.92/1.57 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.92/1.57 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.92/1.57 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.92/1.57 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 0.92/1.57 , Y ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.92/1.57 ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.92/1.57 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse
% 0.92/1.57 ( X, Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oplus__class_Oplus( X
% 0.92/1.57 , Y, Z ) ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Rings_Oinverse__class_Oinverse
% 0.92/1.57 ( X, Y ) ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.57 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.92/1.57 ) ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 0.92/1.57 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ominus__class_Ominus(
% 0.92/1.57 X, Z, Y ) ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , c_Groups_Otimes__class_Otimes( X, Y, c_Rings_Oinverse__class_Oinverse(
% 0.92/1.57 X, Y ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , c_Groups_Otimes__class_Otimes( X, c_Rings_Oinverse__class_Oinverse( X,
% 0.92/1.57 Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.92/1.57 ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) }
% 0.92/1.57 .
% 0.92/1.57 { ! class_Fields_Ofield( X ), c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) }
% 0.92/1.57 .
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.92/1.57 Y ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X )
% 0.92/1.57 , Y ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Z
% 0.92/1.57 , Y ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), ! c_Groups_Otimes__class_Otimes( X, Z
% 0.92/1.57 , Y ) = c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse
% 0.92/1.57 ( X, Z ) = Y }.
% 0.92/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.92/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.92/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 0.92/1.57 , Y ) ) = Y }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.92/1.57 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 0.92/1.57 = Y }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.92/1.57 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.92/1.57 ( X ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 0.92/1.57 X, Y ) ) = Y }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.92/1.57 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.92/1.57 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 0.92/1.57 ( X, c_Groups_Otimes__class_Otimes( X, Y, Z ) ) =
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, c_Rings_Oinverse__class_Oinverse( X, Z
% 0.92/1.57 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.92/1.57 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.57 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 0.92/1.57 , Y = c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.57 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 0.92/1.57 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 0.92/1.57 = c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.57 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.92/1.57 , Y ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 0.92/1.57 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.92/1.57 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.92/1.57 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.92/1.57 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.92/1.57 , Y ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.92/1.57 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.92/1.57 .
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.92/1.57 ( X ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.92/1.57 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.92/1.57 .
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.57 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.57 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Y, Z ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Z, c_Rings_Oinverse__class_Oinverse( X
% 0.92/1.57 , Y ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.92/1.57 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.92/1.57 ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.57 ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.57 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.92/1.57 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.57 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.92/1.57 c_Polynomial_Opdivmod__rel( X, W, U, T, Z ), c_Polynomial_Opdivmod__rel(
% 0.92/1.57 X, W, c_Polynomial_Osmult( X, Y, U ), c_Polynomial_Osmult( X,
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ), T ), Z ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.92/1.57 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.92/1.57 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.92/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.92/1.57 X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X
% 0.92/1.57 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.92/1.57 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.92/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.92/1.57 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.92/1.57 }.
% 0.92/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.57 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 0.92/1.57 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 0.92/1.57 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.92/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.57 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 0.92/1.57 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.92/1.57 ), c_Groups_Ominus__class_Ominus( X, Y, Z ) ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 0.92/1.57 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.92/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) ), T ) =
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Otimes__class_Otimes( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.92/1.57 ), c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X
% 0.92/1.57 , Y, Z ), T ) ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.92/1.57 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 0.92/1.57 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 0.92/1.57 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.92/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.92/1.57 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 0.92/1.57 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.92/1.57 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.92/1.57 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.92/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 0.92/1.57 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.57 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.92/1.57 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.92/1.57 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 X ) }.
% 0.92/1.57 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.57 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 0.92/1.57 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.92/1.57 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.92/1.57 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 0.92/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.92/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.92/1.57 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Y ) }.
% 0.92/1.57 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.92/1.57 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Z ) }.
% 0.92/1.57 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 0.92/1.57 , Z, Y ) }.
% 0.92/1.57 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.92/1.57 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 0.92/1.57 ) }.
% 0.92/1.57 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.92/1.57 , Y ) }.
% 0.92/1.57 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.92/1.57 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.92/1.57 ) }.
% 0.92/1.57 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.92/1.57 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.57 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 0.92/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.92/1.57 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.92/1.57 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, T, Z ), c_Groups_Otimes__class_Otimes(
% 0.92/1.57 X, Y, Z ) ), Z = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.92/1.57 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.57 c_Rings_Odvd__class_Odvd( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.92/1.57 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.92/1.57 c_Rings_Odvd__class_Odvd( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.92/1.57 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.92/1.57 c_Groups_Otimes__class_Otimes( X, T, Z ), c_Groups_Otimes__class_Otimes(
% 0.92/1.57 X, T, Y ) ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.92/1.58 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.92/1.58 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.92/1.58 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.92/1.58 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.92/1.58 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.92/1.58 ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.92/1.58 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ), c_Rings_Odvd__class_Odvd(
% 0.92/1.58 X, Z, Y ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.92/1.58 c_Groups_Otimes__class_Otimes( X, Z, T ), Y ), c_Rings_Odvd__class_Odvd(
% 0.92/1.58 X, Z, Y ) }.
% 0.92/1.58 { ! class_Rings_Odvd( X ), ! Z = c_Groups_Otimes__class_Otimes( X, Y, T ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.58 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 0.92/1.58 c_Groups_Otimes__class_Otimes( X, Z, U ), c_Groups_Otimes__class_Otimes(
% 0.92/1.58 X, Y, T ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.58 Y ), c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Otimes__class_Otimes( X, T
% 0.92/1.58 , Y ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.58 Y ), c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Otimes__class_Otimes( X, Y
% 0.92/1.58 , T ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.58 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.58 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.58 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.92/1.58 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.92/1.58 ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.58 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.92/1.58 Z, T ) }.
% 0.92/1.58 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.92/1.58 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.92/1.58 c_Polynomial_Odegree( X, Y ) ), ! c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ), Y, Z ), Z = Y }.
% 0.92/1.58 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.92/1.58 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.92/1.58 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.92/1.58 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 0.92/1.58 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 0.92/1.58 X, T, Z ), Y ) }.
% 0.92/1.58 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 0.92/1.58 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.92/1.58 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ), Z, T ), c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Opoly__gcd( X, Y, T ) ) }.
% 0.92/1.58 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.92/1.58 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.92/1.58 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ), T, Z ), ! c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ), T, Y ), c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.92/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.58 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.58 X ) }.
% 0.92/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 0.92/1.58 Z ) = c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.58 ) }.
% 0.92/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.58 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.58 X ) }.
% 0.92/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.58 ), ! c_Rings_Odvd__class_Odvd( X, Z, c_Divides_Odiv__class_Omod( X, T, Y
% 0.92/1.58 ) ), c_Rings_Odvd__class_Odvd( X, Z, T ) }.
% 0.92/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.58 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 0.92/1.58 , c_Divides_Odiv__class_Omod( X, T, Y ) ) }.
% 0.92/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.58 ), c_Divides_Odiv__class_Omod( X, c_Divides_Odiv__class_Omod( X, T, Y )
% 0.92/1.58 , Z ) = c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.92/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.58 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 0.92/1.58 , c_Divides_Odiv__class_Omod( X, Y, T ) ) }.
% 0.92/1.58 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, T,
% 0.92/1.58 c_Divides_Odiv__class_Omod( X, Z, Y ) ), ! c_Rings_Odvd__class_Odvd( X, T
% 0.92/1.58 , Y ), c_Rings_Odvd__class_Odvd( X, T, Z ) }.
% 0.92/1.58 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha23( X
% 0.92/1.58 , Y, T ) }.
% 0.92/1.58 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha46( X
% 0.92/1.58 , Y, Z, T ) }.
% 0.92/1.58 { ! class_Fields_Ofield( X ), ! alpha23( X, Y, T ), ! alpha46( X, Y, Z, T )
% 0.92/1.58 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 0.92/1.58 ( X, T, Z ), Y ) }.
% 0.92/1.58 { ! alpha46( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.92/1.58 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha46( X, Y, Z, T ) }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha46( X
% 0.92/1.58 , Y, Z, T ) }.
% 0.92/1.58 { ! alpha23( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.92/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { Z = c_Groups_Ozero__class_Ozero( X ), alpha23( X, Y, Z ) }.
% 0.92/1.58 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha23( X
% 0.92/1.58 , Y, Z ) }.
% 0.92/1.58 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.92/1.58 ( X ), Z, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X )
% 0.92/1.58 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree
% 0.92/1.58 ( X, Z ), c_Polynomial_Odegree( X, Y ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.92/1.58 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.58 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.92/1.58 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.92/1.58 c_Groups_Otimes__class_Otimes( X, W, Y ) ), T ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.92/1.58 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.58 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.92/1.58 c_Groups_Otimes__class_Otimes( X, W, Y ) ), T ) ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.92/1.58 }.
% 0.92/1.58 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.92/1.58 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.58 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.92/1.58 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.92/1.58 c_Groups_Otimes__class_Otimes( X, W, Y ) ), T ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.92/1.58 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.58 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.92/1.58 c_Groups_Otimes__class_Otimes( X, W, Y ) ), T ) ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.92/1.58 }.
% 0.92/1.58 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 0.92/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.92/1.58 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X )
% 0.92/1.58 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.92/1.58 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y )
% 0.92/1.58 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 0.92/1.58 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.92/1.58 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 0.92/1.58 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 0.92/1.58 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.58 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.58 tc_Nat_Onat, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) )
% 0.92/1.58 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.58 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.58 tc_Nat_Onat, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) )
% 0.92/1.58 }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.58 ( tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.92/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.92/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.92/1.58 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.92/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 0.92/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.92/1.58 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.92/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.92/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.58 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.92/1.58 ) }.
% 0.92/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.58 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 0.92/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ),
% 0.92/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.92/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.58 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.58 tc_Nat_Onat, X, Z ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) )
% 0.92/1.58 }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.58 tc_Nat_Onat, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) )
% 0.92/1.58 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd
% 0.92/1.58 ( tc_Nat_Onat, Y, X ) }.
% 0.92/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.58 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 0.92/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ), X ), Y =
% 0.92/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.92/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.58 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.58 tc_Nat_Onat, X, Y ), X ) }.
% 0.92/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.58 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 0.92/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ), X ), Y =
% 0.92/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.92/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.58 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.92/1.58 tc_Nat_Onat, Y, X ), X ) }.
% 0.92/1.58 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.92/1.58 Z, c_Groups_Otimes__class_Otimes( X, Y, T ) ) ), hBOOL( hAPP( Z, skol23(
% 0.92/1.58 U, W, Z ) ) ) }.
% 0.92/1.58 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.92/1.58 Z, c_Groups_Otimes__class_Otimes( X, Y, T ) ) ), c_Rings_Odvd__class_Odvd
% 0.92/1.58 ( X, Y, c_Groups_Oplus__class_Oplus( X, skol23( X, Y, Z ),
% 0.92/1.58 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.92/1.58 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 0.92/1.58 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 0.92/1.58 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 0.92/1.58 hAPP( Z, c_Groups_Otimes__class_Otimes( X, Y, skol27( X, Y, Z ) ) ) ) }.
% 0.92/1.58 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ), Z, Y ), alpha66( X, Y, Z, T ), ! Y =
% 0.92/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 0.92/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.92/1.58 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 0.92/1.58 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ), Z, Y ), alpha66( X, Y, Z, T ), ! hAPP(
% 0.92/1.58 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.92/1.58 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 0.92/1.58 .
% 0.92/1.58 { ! alpha66( X, Y, Z, T ), alpha67( X, Y, Z, T ), alpha64( X, Y, T ) }.
% 0.92/1.58 { ! alpha66( X, Y, Z, T ), alpha67( X, Y, Z, T ), ! hAPP(
% 0.92/1.58 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.92/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.58 { ! alpha67( X, Y, Z, T ), alpha66( X, Y, Z, T ) }.
% 0.92/1.58 { ! alpha64( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.92/1.58 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.58 alpha66( X, Y, Z, T ) }.
% 0.92/1.58 { ! alpha67( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.92/1.58 ( X ), Z, T ), alpha68( X, Y, Z, T ) }.
% 0.92/1.58 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, T ), alpha67( X, Y
% 0.92/1.58 , Z, T ) }.
% 0.92/1.58 { ! alpha68( X, Y, Z, T ), alpha67( X, Y, Z, T ) }.
% 0.92/1.58 { ! alpha68( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.92/1.58 ), skol24( X, Y, U, W ), Y ) }.
% 0.92/1.58 { ! alpha68( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.92/1.58 ), skol24( X, Y, U, T ), T ) }.
% 0.92/1.58 { ! alpha68( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.92/1.58 ( X ), skol24( X, Y, Z, T ), Z ) }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Y ), !
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, T ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Z ), alpha68( X, Y
% 0.92/1.58 , Z, T ) }.
% 0.92/1.58 { ! alpha64( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! alpha64( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 0.92/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha64( X, Y, Z
% 0.92/1.58 ) }.
% 0.92/1.58 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ), c_Power_Opower__class_Opower(
% 0.92/1.58 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 0.92/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.92/1.58 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z, Y
% 0.92/1.58 ) ) ), Y ) }.
% 0.92/1.58 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 0.92/1.58 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.58 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha24( X, Y ), Y = X }
% 0.92/1.58 .
% 0.92/1.58 { ! alpha24( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.58 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.58 { ! alpha24( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.58 { ! alpha24( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.58 ( tc_Nat_Onat, X, Y ), alpha24( X, Y ) }.
% 0.92/1.58 { ! alpha25( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.58 { ! alpha25( X, Y ), ! Y = X }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha25( X, Y ) }
% 0.92/1.58 .
% 0.92/1.58 { ! alpha25( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.58 { ! alpha25( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.58 ( tc_Nat_Onat, X, Y ), alpha25( X, Y ) }.
% 0.92/1.58 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.58 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.92/1.58 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.58 ( tc_Nat_Onat, Y, X ), Y = X }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.92/1.58 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Nat_Onat, Y, Z ) }.
% 0.92/1.58 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Nat_Onat, Y, Z ) }.
% 0.92/1.58 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.92/1.58 ( tc_Nat_Onat, Z, Y ) }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.92/1.58 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.92/1.58 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.92/1.58 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.58 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.92/1.58 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.92/1.58 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Enum_Oenum( tc_HOL_Obool ) }.
% 0.92/1.58 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.92/1.58 { ! class_Enum_Oenum( Y ), ! class_Enum_Oenum( X ), class_Enum_Oenum(
% 0.92/1.58 tc_fun( Y, X ) ) }.
% 0.92/1.58 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.92/1.58 ( tc_fun( Y, X ) ) }.
% 0.92/1.58 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.92/1.58 ) ) }.
% 0.92/1.58 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.92/1.58 .
% 0.92/1.58 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.92/1.58 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.92/1.58 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.92/1.58 { ! class_Enum_Oenum( Y ), ! class_HOL_Oequal( X ), class_HOL_Oequal(
% 0.92/1.58 tc_fun( Y, X ) ) }.
% 0.92/1.58 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.92/1.58 tc_Nat_Onat ) }.
% 0.92/1.58 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.92/1.58 { class_HOL_Oequal( tc_Nat_Onat ) }.
% 0.92/1.58 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.92/1.58 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.92/1.58 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.92/1.58 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.92/1.58 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.92/1.58 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.92/1.58 { class_HOL_Oequal( tc_HOL_Obool ) }.
% 0.92/1.58 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.92/1.58 tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { class_HOL_Oequal( tc_Complex_Ocomplex ) }.
% 0.92/1.58 { ! class_Rings_Oidom( X ),
% 0.92/1.58 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.58 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.92/1.58 ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.58 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.92/1.58 X ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.58 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.92/1.58 ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.58 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.92/1.58 }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.58 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.58 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.58 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.58 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.92/1.58 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.58 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.58 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.58 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.58 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.58 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.92/1.58 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.92/1.58 ( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.92/1.58 ( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 0.92/1.58 ( X ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.92/1.58 }.
% 0.92/1.58 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.92/1.58 ) ) }.
% 0.92/1.58 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.92/1.58 .
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), class_HOL_Oequal(
% 0.92/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.58 { ! hBOOL( hAPP( hAPP( c_fequal, Y ), X ) ), Y = X }.
% 0.92/1.58 { ! Y = X, hBOOL( hAPP( hAPP( c_fequal, Y ), X ) ) }.
% 0.92/1.58 { ! hBOOL( c_fFalse ) }.
% 0.92/1.58 { hBOOL( c_fTrue ) }.
% 0.92/1.58 { ! c_Polynomial_OpCons( tc_Complex_Ocomplex, v_d____, v_ds____ ) =
% 0.92/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.92/1.58 }.
% 0.92/1.58
% 0.92/1.58 *** allocated 15000 integers for clauses
% 0.92/1.58 *** allocated 22500 integers for clauses
% 0.92/1.58 *** allocated 33750 integers for clauses
% 0.92/1.58 *** allocated 50625 integers for clauses
% 0.92/1.58 *** allocated 75937 integers for clauses
% 0.92/1.58 percentage equality = 0.266566, percentage horn = 0.881553
% 0.92/1.58 This is a problem with some equality
% 0.92/1.58
% 0.92/1.58
% 0.92/1.58
% 0.92/1.58 Options Used:
% 0.92/1.58
% 0.92/1.58 useres = 1
% 0.92/1.58 useparamod = 1
% 0.92/1.58 useeqrefl = 1
% 0.92/1.58 useeqfact = 1
% 0.92/1.58 usefactor = 1
% 0.92/1.58 usesimpsplitting = 0
% 0.92/1.58 usesimpdemod = 5
% 0.92/1.58 usesimpres = 3
% 0.92/1.58
% 0.92/1.58 resimpinuse = 1000
% 0.92/1.58 resimpclauses = 20000
% 0.92/1.58 substype = eqrewr
% 0.92/1.58 backwardsubs = 1
% 0.92/1.58 selectoldest = 5
% 0.92/1.58
% 0.92/1.58 litorderings [0] = split
% 0.92/1.58 litorderings [1] = extend the termordering, first sorting on arguments
% 0.92/1.58
% 0.92/1.58 termordering = kbo
% 0.92/1.58
% 0.92/1.58 litapriori = 0
% 0.92/1.58 termapriori = 1
% 0.92/1.58 litaposteriori = 0
% 0.92/1.58 termaposteriori = 0
% 0.92/1.58 demodaposteriori = 0
% 0.92/1.58 ordereqreflfact = 0
% 0.92/1.58
% 0.92/1.58 litselect = negord
% 0.92/1.58
% 0.92/1.58 maxweight = 15
% 0.92/1.58 maxdepth = 30000
% 0.92/1.58 maxlength = 115
% 0.92/1.58 maxnrvars = 195
% 0.92/1.58 excuselevel = 1
% 0.92/1.58 increasemaxweight = 1
% 0.92/1.58
% 0.92/1.58 maxselected = 10000000
% 0.92/1.58 maxnrclauses = 10000000
% 0.92/1.58
% 0.92/1.58 showgenerated = 0
% 0.92/1.58 showkept = 0
% 0.92/1.58 showselected = 0
% 0.92/1.58 showdeleted = 0
% 0.92/1.58 showresimp = 1
% 0.92/1.58 showstatus = 2000
% 0.92/1.58
% 0.92/1.58 prologoutput = 0
% 0.92/1.58 nrgoals = 5000000
% 0.92/1.58 totalproof = 1
% 0.92/1.58
% 0.92/1.58 Symbols occurring in the translation:
% 0.92/1.58
% 0.92/1.58 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.92/1.58 . [1, 2] (w:1, o:199, a:1, s:1, b:0),
% 0.92/1.58 ! [4, 1] (w:0, o:107, a:1, s:1, b:0),
% 0.92/1.58 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.92/1.58 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.92/1.58 hAPP [38, 2] (w:1, o:223, a:1, s:1, b:0),
% 0.92/1.58 v_d____ [39, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.92/1.58 tc_Complex_Ocomplex [40, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.92/1.58 c_Groups_Ozero__class_Ozero [41, 1] (w:1, o:112, a:1, s:1, b:0),
% 0.92/1.58 v_ds____ [43, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.92/1.58 c_Polynomial_OpCons [44, 3] (w:1, o:254, a:1, s:1, b:0),
% 0.92/1.58 c_Polynomial_Opoly [45, 2] (w:1, o:224, a:1, s:1, b:0),
% 0.92/1.58 class_Groups_Ozero [47, 1] (w:1, o:118, a:1, s:1, b:0),
% 0.92/1.58 tc_Polynomial_Opoly [48, 1] (w:1, o:123, a:1, s:1, b:0),
% 0.92/1.58 class_Rings_Ocomm__semiring__0 [53, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.92/1.58 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [54, 3] (w:1
% 0.92/1.58 , o:255, a:1, s:1, b:0),
% 0.92/1.58 v_p [56, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.92/1.58 c_Polynomial_Opoly__rec [61, 5] (w:1, o:344, a:1, s:1, b:0),
% 0.92/1.58 c_fequal [63, 0] (w:1, o:44, a:1, s:1, b:0),
% 0.92/1.58 c_If [64, 4] (w:1, o:314, a:1, s:1, b:0),
% 0.92/1.58 v_c____ [65, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.92/1.58 class_Int_Oring__char__0 [66, 1] (w:1, o:149, a:1, s:1, b:0),
% 0.92/1.58 class_Rings_Oidom [67, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.92/1.58 v_cs____ [70, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.92/1.58 c_Polynomial_Oorder [71, 3] (w:1, o:253, a:1, s:1, b:0),
% 0.92/1.58 tc_Nat_Onat [72, 0] (w:1, o:47, a:1, s:1, b:0),
% 0.92/1.58 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [74, 3] (w:1, o:
% 0.92/1.58 256, a:1, s:1, b:0),
% 0.92/1.58 c_Polynomial_Osynthetic__div [77, 3] (w:1, o:257, a:1, s:1, b:0),
% 0.92/1.58 c_Polynomial_Opcompose [79, 3] (w:1, o:258, a:1, s:1, b:0),
% 0.92/1.58 c_Polynomial_Omonom [80, 3] (w:1, o:259, a:1, s:1, b:0),
% 0.92/1.58 hBOOL [82, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.92/1.58 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [86, 2] (w:1, o:225
% 0.92/1.58 , a:1, s:1, b:0),
% 0.92/1.58 c_Nat_OSuc [89, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.92/1.58 c_Polynomial_Odegree [91, 2] (w:1, o:227, a:1, s:1, b:0),
% 0.92/1.58 class_HOL_Oequal [92, 1] (w:1, o:148, a:1, s:1, b:0),
% 0.92/1.58 c_HOL_Oequal__class_Oequal [93, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.92/1.58 c_Groups_Oplus__class_Oplus [94, 3] (w:1, o:260, a:1, s:1, b:0),
% 0.92/1.58 c_Polynomial_Ocoeff [96, 2] (w:1, o:226, a:1, s:1, b:0),
% 0.92/1.58 c_Polynomial_Osmult [97, 3] (w:1, o:261, a:1, s:1, b:0),
% 0.92/1.58 class_Groups_Ocancel__semigroup__add [99, 1] (w:1, o:127, a:1, s:1
% 0.92/1.58 , b:0),
% 0.92/1.58 class_Groups_Ocancel__ab__semigroup__add [100, 1] (w:1, o:128, a:1
% 0.92/1.58 , s:1, b:0),
% 0.92/1.58 class_Groups_Ocomm__monoid__add [101, 1] (w:1, o:129, a:1, s:1, b:0)
% 0.92/1.58 ,
% 0.92/1.58 class_Groups_Oab__semigroup__add [102, 1] (w:1, o:130, a:1, s:1, b:0)
% 0.92/1.58 ,
% 0.92/1.58 class_Groups_Omonoid__add [105, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.92/1.58 class_Groups_Olinordered__ab__group__add [106, 1] (w:1, o:131, a:1
% 0.92/1.58 , s:1, b:0),
% 0.92/1.58 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.92/1.58 111, 1] (w:1, o:188, a:1, s:1, b:0),
% 0.92/1.58 class_Rings_Ocomm__semiring__1 [116, 1] (w:1, o:155, a:1, s:1, b:0),
% 0.92/1.58
% 0.92/1.58 c_Groups_Otimes__class_Otimes [119, 3] (w:1, o:262, a:1, s:1, b:0),
% 0.92/1.58 c_Nat_Onat_Onat__size [121, 1] (w:1, o:189, a:1, s:1, b:0),
% 0.92/1.58 c_Nat_Onat_Onat__case [122, 3] (w:1, o:263, a:1, s:1, b:0),
% 0.92/1.58 c_Nat_Osize__class_Osize [123, 2] (w:1, o:228, a:1, s:1, b:0),
% 0.92/1.58 c_Orderings_Oord__class_Oless__eq [124, 3] (w:1, o:251, a:1, s:1, b:0
% 0.92/1.58 ),
% 0.92/1.58 class_Groups_Oab__semigroup__mult [131, 1] (w:1, o:133, a:1, s:1, b:0
% 0.92/1.58 ),
% 0.92/1.58 class_Rings_Olinordered__ring [132, 1] (w:1, o:156, a:1, s:1, b:0),
% 0.92/1.58 class_Rings_Olinordered__ring__strict [133, 1] (w:1, o:157, a:1, s:1
% 0.92/1.58 , b:0),
% 0.92/1.58 class_Groups_Oordered__ab__semigroup__add__imp__le [136, 1] (w:1, o:
% 0.92/1.58 134, a:1, s:1, b:0),
% 0.92/1.58 class_Groups_Oordered__ab__semigroup__add [137, 1] (w:1, o:135, a:1
% 0.92/1.58 , s:1, b:0),
% 0.92/1.58 class_Groups_Oordered__comm__monoid__add [140, 1] (w:1, o:136, a:1
% 0.92/1.58 , s:1, b:0),
% 0.92/1.58 class_Rings_Oordered__cancel__semiring [143, 1] (w:1, o:159, a:1, s:1
% 0.92/1.58 , b:0),
% 0.92/1.58 class_Rings_Oordered__ring [144, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.92/1.58 class_Rings_Oordered__semiring [145, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.92/1.58
% 0.92/1.58 class_Rings_Omult__zero [146, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.92/1.58 class_Rings_Oring__no__zero__divisors [147, 1] (w:1, o:170, a:1, s:1
% 0.92/1.58 , b:0),
% 0.92/1.58 class_Rings_Ono__zero__divisors [148, 1] (w:1, o:158, a:1, s:1, b:0)
% 0.92/1.58 ,
% 0.92/1.58 class_Rings_Osemiring [150, 1] (w:1, o:174, a:1, s:1, b:0),
% 0.92/1.58 class_Rings_Ocomm__semiring [151, 1] (w:1, o:175, a:1, s:1, b:0),
% 0.92/1.58 class_Rings_Oordered__comm__semiring [152, 1] (w:1, o:176, a:1, s:1
% 0.92/1.58 , b:0),
% 0.92/1.58 class_Orderings_Opreorder [153, 1] (w:1, o:192, a:1, s:1, b:0),
% 0.92/1.58 class_RealVector_Oreal__normed__algebra [156, 1] (w:1, o:177, a:1, s:
% 0.92/1.58 1, b:0),
% 0.92/1.58 class_Orderings_Oord [159, 1] (w:1, o:190, a:1, s:1, b:0),
% 0.92/1.58 tc_fun [160, 2] (w:1, o:238, a:1, s:1, b:0),
% 0.92/1.58 class_Orderings_Olinorder [161, 1] (w:1, o:193, a:1, s:1, b:0),
% 0.92/1.58 class_Orderings_Oorder [162, 1] (w:1, o:191, a:1, s:1, b:0),
% 0.92/1.58 c_Orderings_Oord__class_Oless [165, 3] (w:1, o:252, a:1, s:1, b:0),
% 0.92/1.58 c_Polynomial_OAbs__poly [166, 2] (w:1, o:239, a:1, s:1, b:0),
% 0.92/1.58 c_fFalse [167, 0] (w:1, o:92, a:1, s:1, b:0),
% 0.92/1.58 c_HOL_Obool_Obool__size [168, 1] (w:1, o:194, a:1, s:1, b:0),
% 0.92/1.58 c_fTrue [169, 0] (w:1, o:93, a:1, s:1, b:0),
% 0.92/1.58 class_Rings_Olinordered__idom [172, 1] (w:1, o:162, a:1, s:1, b:0),
% 0.92/1.58 class_Groups_Oordered__cancel__ab__semigroup__add [173, 1] (w:1, o:
% 0.92/1.58 137, a:1, s:1, b:0),
% 0.92/1.58 class_Rings_Olinordered__comm__semiring__strict [174, 1] (w:1, o:163
% 0.92/1.58 , a:1, s:1, b:0),
% 0.92/1.58 class_Rings_Olinordered__semiring__strict [175, 1] (w:1, o:164, a:1
% 0.92/1.58 , s:1, b:0),
% 0.92/1.58 class_Rings_Olinordered__semidom [176, 1] (w:1, o:165, a:1, s:1, b:0)
% 0.92/1.58 ,
% 0.92/1.58 class_Rings_Olinordered__semiring [179, 1] (w:1, o:166, a:1, s:1, b:0
% 0.92/1.58 ),
% 0.92/1.58 class_Fields_Ofield [181, 1] (w:1, o:114, a:1, s:1, b:0),
% 0.92/1.58 c_Polynomial_Opdivmod__rel [182, 5] (w:1, o:345, a:1, s:1, b:0),
% 0.92/1.58 c_Polynomial_Opos__poly [183, 2] (w:1, o:240, a:1, s:1, b:0),
% 0.92/1.58 class_Rings_Olinordered__semiring__1__strict [192, 1] (w:1, o:167, a:
% 0.92/1.58 1, s:1, b:0),
% 0.92/1.58 c_Groups_Oone__class_Oone [193, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.92/1.58 c_Groups_Ominus__class_Ominus [197, 3] (w:1, o:264, a:1, s:1, b:0),
% 0.92/1.58 class_Rings_Olinordered__semiring__1 [198, 1] (w:1, o:168, a:1, s:1
% 0.92/1.58 , b:0),
% 0.92/1.58 class_Groups_Ogroup__add [199, 1] (w:1, o:138, a:1, s:1, b:0),
% 0.92/1.58 class_Groups_Oab__group__add [200, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.92/1.58 class_Groups_Oordered__ab__group__add [201, 1] (w:1, o:140, a:1, s:1
% 0.92/1.58 , b:0),
% 0.92/1.58 class_Rings_Ozero__neq__one [202, 1] (w:1, o:178, a:1, s:1, b:0),
% 0.92/1.58 class_Groups_Ocomm__monoid__mult [203, 1] (w:1, o:141, a:1, s:1, b:0)
% 0.92/1.58 ,
% 0.92/1.58 class_Groups_Omonoid__mult [204, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.92/1.58 class_Groups_Oone [205, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.92/1.58 class_Rings_Ocomm__ring [206, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.92/1.58 class_Rings_Oring [208, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.92/1.58 class_Rings_Oring__1 [210, 1] (w:1, o:172, a:1, s:1, b:0),
% 0.92/1.58 class_Rings_Ocomm__ring__1 [211, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.92/1.58 c_Groups_Ouminus__class_Ouminus [212, 2] (w:1, o:241, a:1, s:1, b:0)
% 0.92/1.58 ,
% 0.92/1.58 class_Rings_Oring__1__no__zero__divisors [213, 1] (w:1, o:173, a:1
% 0.92/1.58 , s:1, b:0),
% 0.92/1.58 c_Rings_Oinverse__class_Odivide [214, 3] (w:1, o:265, a:1, s:1, b:0)
% 0.92/1.58 ,
% 0.92/1.58 class_Lattices_Oboolean__algebra [215, 1] (w:1, o:196, a:1, s:1, b:0)
% 0.92/1.58 ,
% 0.92/1.58 class_RealVector_Oreal__normed__field [216, 1] (w:1, o:179, a:1, s:1
% 0.92/1.58 , b:0),
% 0.92/1.58 class_Rings_Odivision__ring [217, 1] (w:1, o:180, a:1, s:1, b:0),
% 0.92/1.58 class_Rings_Odivision__ring__inverse__zero [218, 1] (w:1, o:181, a:1
% 0.92/1.58 , s:1, b:0),
% 0.92/1.58 class_RealVector_Oreal__field [219, 1] (w:1, o:182, a:1, s:1, b:0),
% 0.92/1.58 class_Lattices_Oab__semigroup__idem__mult [220, 1] (w:1, o:195, a:1
% 0.92/1.58 , s:1, b:0),
% 0.92/1.58 class_Groups_Ominus [223, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.92/1.58 class_Groups_Ouminus [224, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.92/1.58 class_Fields_Olinordered__field__inverse__zero [225, 1] (w:1, o:115
% 0.92/1.58 , a:1, s:1, b:0),
% 0.92/1.58 class_Fields_Olinordered__field [226, 1] (w:1, o:116, a:1, s:1, b:0)
% 0.92/1.58 ,
% 0.92/1.58 class_Fields_Ofield__inverse__zero [228, 1] (w:1, o:117, a:1, s:1, b:
% 0.92/1.58 0),
% 0.92/1.58 c_Divides_Odiv__class_Omod [229, 3] (w:1, o:266, a:1, s:1, b:0),
% 0.92/1.58 c_Groups_Osgn__class_Osgn [230, 2] (w:1, o:242, a:1, s:1, b:0),
% 0.92/1.58 class_RealVector_Oreal__normed__vector [231, 1] (w:1, o:183, a:1, s:1
% 0.92/1.58 , b:0),
% 0.92/1.58 class_RealVector_Oreal__normed__algebra__1 [232, 1] (w:1, o:184, a:1
% 0.92/1.58 , s:1, b:0),
% 0.92/1.58 class_Groups_Osgn__if [233, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.92/1.58 class_RealVector_Oreal__normed__div__algebra [234, 1] (w:1, o:185, a:
% 0.92/1.58 1, s:1, b:0),
% 0.92/1.58 class_Divides_Osemiring__div [235, 1] (w:1, o:198, a:1, s:1, b:0),
% 0.92/1.58 class_Divides_Oring__div [237, 1] (w:1, o:197, a:1, s:1, b:0),
% 0.92/1.58 c_Polynomial_Opoly__gcd [238, 3] (w:1, o:267, a:1, s:1, b:0),
% 0.92/1.58 c_Rings_Oinverse__class_Oinverse [239, 2] (w:1, o:243, a:1, s:1, b:0)
% 0.92/1.58 ,
% 0.92/1.58 c_Rings_Odvd__class_Odvd [240, 3] (w:1, o:268, a:1, s:1, b:0),
% 0.92/1.58 class_Rings_Odvd [241, 1] (w:1, o:186, a:1, s:1, b:0),
% 0.92/1.58 class_Rings_Osemiring__0 [244, 1] (w:1, o:187, a:1, s:1, b:0),
% 0.92/1.58 c_Power_Opower__class_Opower [245, 3] (w:1, o:269, a:1, s:1, b:0),
% 0.92/1.58 class_Groups_Ocancel__comm__monoid__add [247, 1] (w:1, o:147, a:1, s:
% 0.92/1.58 1, b:0),
% 0.92/1.58 tc_HOL_Obool [248, 0] (w:1, o:105, a:1, s:1, b:0),
% 0.92/1.58 class_Enum_Oenum [249, 1] (w:1, o:113, a:1, s:1, b:0),
% 0.92/1.58 alpha1 [251, 2] (w:1, o:244, a:1, s:1, b:1),
% 0.92/1.58 alpha2 [252, 2] (w:1, o:245, a:1, s:1, b:1),
% 0.92/1.58 alpha3 [253, 3] (w:1, o:276, a:1, s:1, b:1),
% 3.37/3.80 alpha4 [254, 3] (w:1, o:284, a:1, s:1, b:1),
% 3.37/3.80 alpha5 [255, 4] (w:1, o:323, a:1, s:1, b:1),
% 3.37/3.80 alpha6 [256, 4] (w:1, o:333, a:1, s:1, b:1),
% 3.37/3.80 alpha7 [257, 2] (w:1, o:246, a:1, s:1, b:1),
% 3.37/3.80 alpha8 [258, 3] (w:1, o:285, a:1, s:1, b:1),
% 3.37/3.80 alpha9 [259, 3] (w:1, o:286, a:1, s:1, b:1),
% 3.37/3.80 alpha10 [260, 3] (w:1, o:287, a:1, s:1, b:1),
% 3.37/3.80 alpha11 [261, 3] (w:1, o:288, a:1, s:1, b:1),
% 3.37/3.80 alpha12 [262, 3] (w:1, o:289, a:1, s:1, b:1),
% 3.37/3.80 alpha13 [263, 3] (w:1, o:290, a:1, s:1, b:1),
% 3.37/3.80 alpha14 [264, 3] (w:1, o:291, a:1, s:1, b:1),
% 3.37/3.80 alpha15 [265, 3] (w:1, o:292, a:1, s:1, b:1),
% 3.37/3.80 alpha16 [266, 3] (w:1, o:293, a:1, s:1, b:1),
% 3.37/3.80 alpha17 [267, 3] (w:1, o:294, a:1, s:1, b:1),
% 3.37/3.80 alpha18 [268, 3] (w:1, o:295, a:1, s:1, b:1),
% 3.37/3.80 alpha19 [269, 3] (w:1, o:296, a:1, s:1, b:1),
% 3.37/3.80 alpha20 [270, 3] (w:1, o:270, a:1, s:1, b:1),
% 3.37/3.80 alpha21 [271, 3] (w:1, o:271, a:1, s:1, b:1),
% 3.37/3.80 alpha22 [272, 3] (w:1, o:272, a:1, s:1, b:1),
% 3.37/3.80 alpha23 [273, 3] (w:1, o:273, a:1, s:1, b:1),
% 3.37/3.80 alpha24 [274, 2] (w:1, o:247, a:1, s:1, b:1),
% 3.37/3.80 alpha25 [275, 2] (w:1, o:248, a:1, s:1, b:1),
% 3.37/3.80 alpha26 [276, 2] (w:1, o:249, a:1, s:1, b:1),
% 3.37/3.80 alpha27 [277, 2] (w:1, o:250, a:1, s:1, b:1),
% 3.37/3.80 alpha28 [278, 3] (w:1, o:274, a:1, s:1, b:1),
% 3.37/3.80 alpha29 [279, 3] (w:1, o:275, a:1, s:1, b:1),
% 3.37/3.80 alpha30 [280, 4] (w:1, o:334, a:1, s:1, b:1),
% 3.37/3.80 alpha31 [281, 4] (w:1, o:335, a:1, s:1, b:1),
% 3.37/3.80 alpha32 [282, 3] (w:1, o:277, a:1, s:1, b:1),
% 3.37/3.80 alpha33 [283, 3] (w:1, o:278, a:1, s:1, b:1),
% 3.37/3.80 alpha34 [284, 3] (w:1, o:279, a:1, s:1, b:1),
% 3.37/3.80 alpha35 [285, 3] (w:1, o:280, a:1, s:1, b:1),
% 3.37/3.80 alpha36 [286, 3] (w:1, o:281, a:1, s:1, b:1),
% 3.37/3.80 alpha37 [287, 3] (w:1, o:282, a:1, s:1, b:1),
% 3.37/3.80 alpha38 [288, 3] (w:1, o:283, a:1, s:1, b:1),
% 3.37/3.80 alpha39 [289, 4] (w:1, o:336, a:1, s:1, b:1),
% 3.37/3.80 alpha40 [290, 4] (w:1, o:315, a:1, s:1, b:1),
% 3.37/3.80 alpha41 [291, 4] (w:1, o:316, a:1, s:1, b:1),
% 3.37/3.80 alpha42 [292, 4] (w:1, o:317, a:1, s:1, b:1),
% 3.37/3.80 alpha43 [293, 4] (w:1, o:318, a:1, s:1, b:1),
% 3.37/3.80 alpha44 [294, 4] (w:1, o:319, a:1, s:1, b:1),
% 3.37/3.80 alpha45 [295, 3] (w:1, o:297, a:1, s:1, b:1),
% 3.37/3.80 alpha46 [296, 4] (w:1, o:320, a:1, s:1, b:1),
% 3.37/3.80 alpha47 [297, 4] (w:1, o:321, a:1, s:1, b:1),
% 3.37/3.80 alpha48 [298, 3] (w:1, o:298, a:1, s:1, b:1),
% 3.37/3.80 alpha49 [299, 4] (w:1, o:322, a:1, s:1, b:1),
% 3.37/3.80 alpha50 [300, 4] (w:1, o:324, a:1, s:1, b:1),
% 3.37/3.80 alpha51 [301, 4] (w:1, o:325, a:1, s:1, b:1),
% 3.37/3.80 alpha52 [302, 4] (w:1, o:326, a:1, s:1, b:1),
% 3.37/3.80 alpha53 [303, 3] (w:1, o:299, a:1, s:1, b:1),
% 3.37/3.80 alpha54 [304, 4] (w:1, o:327, a:1, s:1, b:1),
% 3.37/3.80 alpha55 [305, 4] (w:1, o:328, a:1, s:1, b:1),
% 3.37/3.80 alpha56 [306, 4] (w:1, o:329, a:1, s:1, b:1),
% 3.37/3.80 alpha57 [307, 4] (w:1, o:330, a:1, s:1, b:1),
% 3.37/3.80 alpha58 [308, 4] (w:1, o:331, a:1, s:1, b:1),
% 3.37/3.80 alpha59 [309, 4] (w:1, o:332, a:1, s:1, b:1),
% 3.37/3.80 alpha60 [310, 4] (w:1, o:337, a:1, s:1, b:1),
% 3.37/3.80 alpha61 [311, 4] (w:1, o:338, a:1, s:1, b:1),
% 3.37/3.80 alpha62 [312, 4] (w:1, o:339, a:1, s:1, b:1),
% 3.37/3.80 alpha63 [313, 3] (w:1, o:300, a:1, s:1, b:1),
% 3.37/3.80 alpha64 [314, 3] (w:1, o:301, a:1, s:1, b:1),
% 3.37/3.80 alpha65 [315, 3] (w:1, o:302, a:1, s:1, b:1),
% 3.37/3.80 alpha66 [316, 4] (w:1, o:340, a:1, s:1, b:1),
% 3.37/3.80 alpha67 [317, 4] (w:1, o:341, a:1, s:1, b:1),
% 3.37/3.80 alpha68 [318, 4] (w:1, o:342, a:1, s:1, b:1),
% 3.37/3.80 skol1 [319, 2] (w:1, o:229, a:1, s:1, b:1),
% 3.37/3.80 skol2 [320, 0] (w:1, o:17, a:1, s:1, b:1),
% 3.37/3.80 skol3 [321, 2] (w:1, o:232, a:1, s:1, b:1),
% 3.37/3.80 skol4 [322, 1] (w:1, o:119, a:1, s:1, b:1),
% 3.37/3.80 skol5 [323, 0] (w:1, o:18, a:1, s:1, b:1),
% 3.37/3.80 skol6 [324, 1] (w:1, o:120, a:1, s:1, b:1),
% 3.37/3.80 skol7 [325, 3] (w:1, o:303, a:1, s:1, b:1),
% 3.37/3.80 skol8 [326, 2] (w:1, o:233, a:1, s:1, b:1),
% 3.37/3.80 skol9 [327, 2] (w:1, o:234, a:1, s:1, b:1),
% 3.37/3.80 skol10 [328, 3] (w:1, o:304, a:1, s:1, b:1),
% 3.37/3.80 skol11 [329, 2] (w:1, o:235, a:1, s:1, b:1),
% 3.37/3.80 skol12 [330, 1] (w:1, o:121, a:1, s:1, b:1),
% 3.37/3.80 skol13 [331, 2] (w:1, o:236, a:1, s:1, b:1),
% 20.55/20.97 skol14 [332, 3] (w:1, o:305, a:1, s:1, b:1),
% 20.55/20.97 skol15 [333, 3] (w:1, o:306, a:1, s:1, b:1),
% 20.55/20.97 skol16 [334, 3] (w:1, o:307, a:1, s:1, b:1),
% 20.55/20.97 skol17 [335, 3] (w:1, o:308, a:1, s:1, b:1),
% 20.55/20.97 skol18 [336, 2] (w:1, o:237, a:1, s:1, b:1),
% 20.55/20.97 skol19 [337, 3] (w:1, o:309, a:1, s:1, b:1),
% 20.55/20.97 skol20 [338, 3] (w:1, o:310, a:1, s:1, b:1),
% 20.55/20.97 skol21 [339, 2] (w:1, o:230, a:1, s:1, b:1),
% 20.55/20.97 skol22 [340, 3] (w:1, o:311, a:1, s:1, b:1),
% 20.55/20.97 skol23 [341, 3] (w:1, o:312, a:1, s:1, b:1),
% 20.55/20.97 skol24 [342, 4] (w:1, o:343, a:1, s:1, b:1),
% 20.55/20.97 skol25 [343, 2] (w:1, o:231, a:1, s:1, b:1),
% 20.55/20.97 skol26 [344, 1] (w:1, o:122, a:1, s:1, b:1),
% 20.55/20.97 skol27 [345, 3] (w:1, o:313, a:1, s:1, b:1).
% 20.55/20.97
% 20.55/20.97
% 20.55/20.97 Starting Search:
% 20.55/20.97
% 20.55/20.97 *** allocated 113905 integers for clauses
% 20.55/20.97 *** allocated 170857 integers for clauses
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97
% 20.55/20.97 Intermediate Status:
% 20.55/20.97 Generated: 2997
% 20.55/20.97 Kept: 2016
% 20.55/20.97 Inuse: 30
% 20.55/20.97 Deleted: 1
% 20.55/20.97 Deletedinuse: 0
% 20.55/20.97
% 20.55/20.97 *** allocated 256285 integers for clauses
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97 *** allocated 170857 integers for termspace/termends
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97 *** allocated 384427 integers for clauses
% 20.55/20.97
% 20.55/20.97 Intermediate Status:
% 20.55/20.97 Generated: 8583
% 20.55/20.97 Kept: 4209
% 20.55/20.97 Inuse: 135
% 20.55/20.97 Deleted: 1
% 20.55/20.97 Deletedinuse: 0
% 20.55/20.97
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97 *** allocated 256285 integers for termspace/termends
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97
% 20.55/20.97 Intermediate Status:
% 20.55/20.97 Generated: 13392
% 20.55/20.97 Kept: 6442
% 20.55/20.97 Inuse: 204
% 20.55/20.97 Deleted: 3
% 20.55/20.97 Deletedinuse: 1
% 20.55/20.97
% 20.55/20.97 *** allocated 576640 integers for clauses
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97
% 20.55/20.97 Intermediate Status:
% 20.55/20.97 Generated: 18589
% 20.55/20.97 Kept: 8452
% 20.55/20.97 Inuse: 263
% 20.55/20.97 Deleted: 4
% 20.55/20.97 Deletedinuse: 2
% 20.55/20.97
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97 *** allocated 384427 integers for termspace/termends
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97
% 20.55/20.97 Intermediate Status:
% 20.55/20.97 Generated: 24283
% 20.55/20.97 Kept: 10754
% 20.55/20.97 Inuse: 305
% 20.55/20.97 Deleted: 9
% 20.55/20.97 Deletedinuse: 3
% 20.55/20.97
% 20.55/20.97 *** allocated 864960 integers for clauses
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97
% 20.55/20.97 Intermediate Status:
% 20.55/20.97 Generated: 31154
% 20.55/20.97 Kept: 12927
% 20.55/20.97 Inuse: 325
% 20.55/20.97 Deleted: 9
% 20.55/20.97 Deletedinuse: 3
% 20.55/20.97
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97 *** allocated 576640 integers for termspace/termends
% 20.55/20.97
% 20.55/20.97 Intermediate Status:
% 20.55/20.97 Generated: 40938
% 20.55/20.97 Kept: 15821
% 20.55/20.97 Inuse: 370
% 20.55/20.97 Deleted: 9
% 20.55/20.97 Deletedinuse: 3
% 20.55/20.97
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97 *** allocated 1297440 integers for clauses
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97
% 20.55/20.97 Intermediate Status:
% 20.55/20.97 Generated: 51492
% 20.55/20.97 Kept: 18278
% 20.55/20.97 Inuse: 414
% 20.55/20.97 Deleted: 10
% 20.55/20.97 Deletedinuse: 3
% 20.55/20.97
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97
% 20.55/20.97 Intermediate Status:
% 20.55/20.97 Generated: 58398
% 20.55/20.97 Kept: 20446
% 20.55/20.97 Inuse: 445
% 20.55/20.97 Deleted: 14
% 20.55/20.97 Deletedinuse: 3
% 20.55/20.97
% 20.55/20.97 Resimplifying clauses:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97
% 20.55/20.97 Intermediate Status:
% 20.55/20.97 Generated: 65874
% 20.55/20.97 Kept: 22454
% 20.55/20.97 Inuse: 500
% 20.55/20.97 Deleted: 336
% 20.55/20.97 Deletedinuse: 3
% 20.55/20.97
% 20.55/20.97 *** allocated 864960 integers for termspace/termends
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97
% 20.55/20.97 Intermediate Status:
% 20.55/20.97 Generated: 73897
% 20.55/20.97 Kept: 24703
% 20.55/20.97 Inuse: 525
% 20.55/20.97 Deleted: 336
% 20.55/20.97 Deletedinuse: 3
% 20.55/20.97
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97 *** allocated 1946160 integers for clauses
% 20.55/20.97
% 20.55/20.97 Intermediate Status:
% 20.55/20.97 Generated: 84610
% 20.55/20.97 Kept: 26824
% 20.55/20.97 Inuse: 540
% 20.55/20.97 Deleted: 336
% 20.55/20.97 Deletedinuse: 3
% 20.55/20.97
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97
% 20.55/20.97 Intermediate Status:
% 20.55/20.97 Generated: 91889
% 20.55/20.97 Kept: 29170
% 20.55/20.97 Inuse: 565
% 20.55/20.97 Deleted: 430
% 20.55/20.97 Deletedinuse: 97
% 20.55/20.97
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97
% 20.55/20.97 Intermediate Status:
% 20.55/20.97 Generated: 95263
% 20.55/20.97 Kept: 31340
% 20.55/20.97 Inuse: 575
% 20.55/20.97 Deleted: 430
% 20.55/20.97 Deletedinuse: 97
% 20.55/20.97
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97
% 20.55/20.97 Intermediate Status:
% 20.55/20.97 Generated: 98838
% 20.55/20.97 Kept: 33600
% 20.55/20.97 Inuse: 585
% 20.55/20.97 Deleted: 430
% 20.55/20.97 Deletedinuse: 97
% 20.55/20.97
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97 *** allocated 1297440 integers for termspace/termends
% 20.55/20.97
% 20.55/20.97 Intermediate Status:
% 20.55/20.97 Generated: 110368
% 20.55/20.97 Kept: 36556
% 20.55/20.97 Inuse: 615
% 20.55/20.97 Deleted: 430
% 20.55/20.97 Deletedinuse: 97
% 20.55/20.97
% 20.55/20.97 Resimplifying inuse:
% 20.55/20.97 Done
% 20.55/20.97
% 20.55/20.97 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 118010
% 65.89/66.28 Kept: 38785
% 65.89/66.28 Inuse: 655
% 65.89/66.28 Deleted: 430
% 65.89/66.28 Deletedinuse: 97
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 122743
% 65.89/66.28 Kept: 41341
% 65.89/66.28 Inuse: 665
% 65.89/66.28 Deleted: 430
% 65.89/66.28 Deletedinuse: 97
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 Resimplifying clauses:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 *** allocated 2919240 integers for clauses
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 129447
% 65.89/66.28 Kept: 43353
% 65.89/66.28 Inuse: 680
% 65.89/66.28 Deleted: 2371
% 65.89/66.28 Deletedinuse: 98
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 135772
% 65.89/66.28 Kept: 45356
% 65.89/66.28 Inuse: 714
% 65.89/66.28 Deleted: 2371
% 65.89/66.28 Deletedinuse: 98
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 144371
% 65.89/66.28 Kept: 47766
% 65.89/66.28 Inuse: 730
% 65.89/66.28 Deleted: 2371
% 65.89/66.28 Deletedinuse: 98
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 155252
% 65.89/66.28 Kept: 50557
% 65.89/66.28 Inuse: 780
% 65.89/66.28 Deleted: 2371
% 65.89/66.28 Deletedinuse: 98
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 161981
% 65.89/66.28 Kept: 52578
% 65.89/66.28 Inuse: 802
% 65.89/66.28 Deleted: 2371
% 65.89/66.28 Deletedinuse: 98
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 *** allocated 1946160 integers for termspace/termends
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 183744
% 65.89/66.28 Kept: 55015
% 65.89/66.28 Inuse: 815
% 65.89/66.28 Deleted: 2371
% 65.89/66.28 Deletedinuse: 98
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 191914
% 65.89/66.28 Kept: 57027
% 65.89/66.28 Inuse: 848
% 65.89/66.28 Deleted: 2371
% 65.89/66.28 Deletedinuse: 98
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 198734
% 65.89/66.28 Kept: 59654
% 65.89/66.28 Inuse: 870
% 65.89/66.28 Deleted: 2371
% 65.89/66.28 Deletedinuse: 98
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 Resimplifying clauses:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 205533
% 65.89/66.28 Kept: 61677
% 65.89/66.28 Inuse: 893
% 65.89/66.28 Deleted: 2399
% 65.89/66.28 Deletedinuse: 98
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 214232
% 65.89/66.28 Kept: 63790
% 65.89/66.28 Inuse: 930
% 65.89/66.28 Deleted: 2399
% 65.89/66.28 Deletedinuse: 98
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 *** allocated 4378860 integers for clauses
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 222938
% 65.89/66.28 Kept: 65809
% 65.89/66.28 Inuse: 971
% 65.89/66.28 Deleted: 2399
% 65.89/66.28 Deletedinuse: 98
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 233386
% 65.89/66.28 Kept: 68427
% 65.89/66.28 Inuse: 1005
% 65.89/66.28 Deleted: 2399
% 65.89/66.28 Deletedinuse: 98
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 261290
% 65.89/66.28 Kept: 71870
% 65.89/66.28 Inuse: 1020
% 65.89/66.28 Deleted: 2399
% 65.89/66.28 Deletedinuse: 98
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 271406
% 65.89/66.28 Kept: 74126
% 65.89/66.28 Inuse: 1045
% 65.89/66.28 Deleted: 2399
% 65.89/66.28 Deletedinuse: 98
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 282527
% 65.89/66.28 Kept: 76248
% 65.89/66.28 Inuse: 1065
% 65.89/66.28 Deleted: 2399
% 65.89/66.28 Deletedinuse: 98
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 *** allocated 2919240 integers for termspace/termends
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 292228
% 65.89/66.28 Kept: 78659
% 65.89/66.28 Inuse: 1105
% 65.89/66.28 Deleted: 2399
% 65.89/66.28 Deletedinuse: 98
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 312475
% 65.89/66.28 Kept: 81290
% 65.89/66.28 Inuse: 1120
% 65.89/66.28 Deleted: 2399
% 65.89/66.28 Deletedinuse: 98
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 Resimplifying clauses:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 321084
% 65.89/66.28 Kept: 83445
% 65.89/66.28 Inuse: 1155
% 65.89/66.28 Deleted: 2519
% 65.89/66.28 Deletedinuse: 98
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 328469
% 65.89/66.28 Kept: 85447
% 65.89/66.28 Inuse: 1195
% 65.89/66.28 Deleted: 2519
% 65.89/66.28 Deletedinuse: 98
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 337251
% 65.89/66.28 Kept: 87631
% 65.89/66.28 Inuse: 1240
% 65.89/66.28 Deleted: 2519
% 65.89/66.28 Deletedinuse: 98
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 65.89/66.28 Done
% 65.89/66.28
% 65.89/66.28
% 65.89/66.28 Intermediate Status:
% 65.89/66.28 Generated: 360689
% 65.89/66.28 Kept: 91445
% 65.89/66.28 Inuse: 1270
% 65.89/66.28 Deleted: 2519
% 65.89/66.28 Deletedinuse: 98
% 65.89/66.28
% 65.89/66.28 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 385316
% 135.36/135.76 Kept: 93986
% 135.36/135.76 Inuse: 1285
% 135.36/135.76 Deleted: 2519
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 408824
% 135.36/135.76 Kept: 96274
% 135.36/135.76 Inuse: 1295
% 135.36/135.76 Deleted: 2519
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 420450
% 135.36/135.76 Kept: 98489
% 135.36/135.76 Inuse: 1305
% 135.36/135.76 Deleted: 2519
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 431606
% 135.36/135.76 Kept: 100659
% 135.36/135.76 Inuse: 1335
% 135.36/135.76 Deleted: 2519
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76 *** allocated 6568290 integers for clauses
% 135.36/135.76 Resimplifying clauses:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 441121
% 135.36/135.76 Kept: 102692
% 135.36/135.76 Inuse: 1362
% 135.36/135.76 Deleted: 2813
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 460057
% 135.36/135.76 Kept: 105125
% 135.36/135.76 Inuse: 1370
% 135.36/135.76 Deleted: 2813
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 480535
% 135.36/135.76 Kept: 107778
% 135.36/135.76 Inuse: 1385
% 135.36/135.76 Deleted: 2813
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 494765
% 135.36/135.76 Kept: 110072
% 135.36/135.76 Inuse: 1410
% 135.36/135.76 Deleted: 2813
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 502969
% 135.36/135.76 Kept: 112096
% 135.36/135.76 Inuse: 1432
% 135.36/135.76 Deleted: 2813
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76 *** allocated 4378860 integers for termspace/termends
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 512309
% 135.36/135.76 Kept: 114097
% 135.36/135.76 Inuse: 1460
% 135.36/135.76 Deleted: 2813
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 529921
% 135.36/135.76 Kept: 117201
% 135.36/135.76 Inuse: 1480
% 135.36/135.76 Deleted: 2813
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 540357
% 135.36/135.76 Kept: 119282
% 135.36/135.76 Inuse: 1500
% 135.36/135.76 Deleted: 2813
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 551951
% 135.36/135.76 Kept: 121342
% 135.36/135.76 Inuse: 1522
% 135.36/135.76 Deleted: 2813
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76 Resimplifying clauses:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 561975
% 135.36/135.76 Kept: 123388
% 135.36/135.76 Inuse: 1530
% 135.36/135.76 Deleted: 2924
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 573669
% 135.36/135.76 Kept: 125439
% 135.36/135.76 Inuse: 1553
% 135.36/135.76 Deleted: 2927
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 580710
% 135.36/135.76 Kept: 127439
% 135.36/135.76 Inuse: 1590
% 135.36/135.76 Deleted: 2932
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 591967
% 135.36/135.76 Kept: 130399
% 135.36/135.76 Inuse: 1592
% 135.36/135.76 Deleted: 2932
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 603219
% 135.36/135.76 Kept: 136380
% 135.36/135.76 Inuse: 1602
% 135.36/135.76 Deleted: 2932
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 615788
% 135.36/135.76 Kept: 138891
% 135.36/135.76 Inuse: 1630
% 135.36/135.76 Deleted: 2934
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 630921
% 135.36/135.76 Kept: 142456
% 135.36/135.76 Inuse: 1655
% 135.36/135.76 Deleted: 2934
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76 Resimplifying clauses:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 640403
% 135.36/135.76 Kept: 145548
% 135.36/135.76 Inuse: 1660
% 135.36/135.76 Deleted: 3455
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 649885
% 135.36/135.76 Kept: 148409
% 135.36/135.76 Inuse: 1687
% 135.36/135.76 Deleted: 3455
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 657323
% 135.36/135.76 Kept: 150559
% 135.36/135.76 Inuse: 1720
% 135.36/135.76 Deleted: 3455
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76
% 135.36/135.76 Intermediate Status:
% 135.36/135.76 Generated: 667811
% 135.36/135.76 Kept: 154303
% 135.36/135.76 Inuse: 1735
% 135.36/135.76 Deleted: 3455
% 135.36/135.76 Deletedinuse: 98
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76 Resimplifying inuse:
% 135.36/135.76 Done
% 135.36/135.76
% 135.36/135.76 *** allocated 9852435 integers for clauses
% 267.09/267.52
% 267.09/267.52 Intermediate Status:
% 267.09/267.52 Generated: 683588
% 267.09/267.52 Kept: 160091
% 267.09/267.52 Inuse: 1755
% 267.09/267.52 Deleted: 3455
% 267.09/267.52 Deletedinuse: 98
% 267.09/267.52
% 267.09/267.52 Resimplifying inuse:
% 267.09/267.52 Done
% 267.09/267.52
% 267.09/267.52
% 267.09/267.52 Intermediate Status:
% 267.09/267.52 Generated: 691945
% 267.09/267.52 Kept: 162187
% 267.09/267.52 Inuse: 1765
% 267.09/267.52 Deleted: 3455
% 267.09/267.52 Deletedinuse: 98
% 267.09/267.52
% 267.09/267.52 Resimplifying inuse:
% 267.09/267.52 Done
% 267.09/267.52
% 267.09/267.52 Resimplifying clauses:
% 267.09/267.52 Done
% 267.09/267.52
% 267.09/267.52 Resimplifying inuse:
% 267.09/267.52 Done
% 267.09/267.52
% 267.09/267.52
% 267.09/267.52 Intermediate Status:
% 267.09/267.52 Generated: 702105
% 267.09/267.52 Kept: 164302
% 267.09/267.52 Inuse: 1795
% 267.09/267.52 Deleted: 3547
% 267.09/267.52 Deletedinuse: 98
% 267.09/267.52
% 267.09/267.52 Resimplifying inuse:
% 267.09/267.52 Done
% 267.09/267.52
% 267.09/267.52 Resimplifying inuse:
% 267.09/267.52 Done
% 267.09/267.52
% 267.09/267.52
% 267.09/267.52 Intermediate Status:
% 267.09/267.52 Generated: 712074
% 267.09/267.52 Kept: 166350
% 267.09/267.52 Inuse: 1820
% 267.09/267.52 Deleted: 3547
% 267.09/267.52 Deletedinuse: 98
% 267.09/267.52
% 267.09/267.52 Resimplifying inuse:
% 267.09/267.52 Done
% 267.09/267.52
% 267.09/267.52
% 267.09/267.52 Intermediate Status:
% 267.09/267.52 Generated: 718907
% 267.09/267.52 Kept: 169096
% 267.09/267.52 Inuse: 1830
% 267.09/267.52 Deleted: 3548
% 267.09/267.52 Deletedinuse: 98
% 267.09/267.52
% 267.09/267.52 Resimplifying inuse:
% 267.09/267.52 Done
% 267.09/267.52
% 267.09/267.52
% 267.09/267.52 Intermediate Status:
% 267.09/267.52 Generated: 729563
% 267.09/267.52 Kept: 174222
% 267.09/267.52 Inuse: 1834
% 267.09/267.52 Deleted: 3548
% 267.09/267.52 Deletedinuse: 98
% 267.09/267.52
% 267.09/267.52 Resimplifying inuse:
% 267.09/267.52 Done
% 267.09/267.52
% 267.09/267.52 Resimplifying inuse:
% 267.09/267.52 Done
% 267.09/267.52
% 267.09/267.52
% 267.09/267.52 Intermediate Status:
% 267.09/267.52 Generated: 738749
% 267.09/267.52 Kept: 176400
% 267.09/267.52 Inuse: 1859
% 267.09/267.52 Deleted: 3549
% 267.09/267.52 Deletedinuse: 99
% 267.09/267.52
% 267.09/267.52 Resimplifying inuse:
% 267.09/267.52 Done
% 267.09/267.52
% 267.09/267.52 Resimplifying inuse:
% 267.09/267.52 Done
% 267.09/267.52
% 267.09/267.52
% 267.09/267.52 Intermediate Status:
% 267.09/267.52 Generated: 747898
% 267.09/267.52 Kept: 178434
% 267.09/267.52 Inuse: 1880
% 267.09/267.52 Deleted: 3549
% 267.09/267.52 Deletedinuse: 99
% 267.09/267.52
% 267.09/267.52 Resimplifying inuse:
% 267.09/267.52 Done
% 267.09/267.52
% 267.09/267.52 Resimplifying inuse:
% 267.09/267.52 Done
% 267.09/267.52
% 267.09/267.52 *** allocated 6568290 integers for termspace/termends
% 267.09/267.52
% 267.09/267.52 Intermediate Status:
% 267.09/267.52 Generated: 756425
% 267.09/267.52 Kept: 180471
% 267.09/267.52 Inuse: 1901
% 267.09/267.52 Deleted: 3549
% 267.09/267.52 Deletedinuse: 99
% 267.09/267.52
% 267.09/267.52 Resimplifying inuse:
% 267.09/267.52 Done
% 267.09/267.52
% 267.09/267.52 Resimplifying inuse:
% 267.09/267.52 Done
% 267.09/267.52
% 267.09/267.52
% 267.09/267.52 Intermediate Status:
% 267.09/267.52 Generated: 763776
% 267.09/267.52 Kept: 182582
% 267.09/267.52 Inuse: 1919
% 267.09/267.52 Deleted: 3549
% 267.09/267.52 Deletedinuse: 99
% 267.09/267.52
% 267.09/267.52 Resimplifying inuse:
% 267.09/267.52 Done
% 267.09/267.52
% 267.09/267.52 Resimplifying clauses:
% 267.09/267.52 Done
% 267.09/267.52
% 267.09/267.52 Resimplifying inuse:
% 267.09/267.52 Done
% 267.09/267.52
% 267.09/267.52
% 267.09/267.52 Intermediate Status:
% 267.09/267.52 Generated: 771085
% 267.09/267.52 Kept: 184596
% 267.09/267.52 Inuse: 1948
% 267.09/267.52 Deleted: 3668
% 267.09/267.52 Deletedinuse: 99
% 267.09/267.52
% 267.09/267.52 Resimplifying inuse:
% 267.09/267.52 Done
% 267.09/267.52
% 267.09/267.52 Resimplifying inuse:
% 267.09/267.52 Done
% 267.09/267.52
% 267.09/267.52
% 267.09/267.52 Intermediate Status:
% 267.09/267.52 Generated: 776822
% 267.09/267.52 Kept: 186764
% 267.09/267.52 Inuse: 1979
% 267.09/267.52 Deleted: 3668
% 267.09/267.53 Deletedinuse: 99
% 267.09/267.53
% 267.09/267.53 Resimplifying inuse:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53 Resimplifying inuse:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53
% 267.09/267.53 Intermediate Status:
% 267.09/267.53 Generated: 782243
% 267.09/267.53 Kept: 188805
% 267.09/267.53 Inuse: 2012
% 267.09/267.53 Deleted: 3676
% 267.09/267.53 Deletedinuse: 100
% 267.09/267.53
% 267.09/267.53 Resimplifying inuse:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53 Resimplifying inuse:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53
% 267.09/267.53 Intermediate Status:
% 267.09/267.53 Generated: 792368
% 267.09/267.53 Kept: 192751
% 267.09/267.53 Inuse: 2032
% 267.09/267.53 Deleted: 3677
% 267.09/267.53 Deletedinuse: 100
% 267.09/267.53
% 267.09/267.53 Resimplifying inuse:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53 Resimplifying inuse:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53
% 267.09/267.53 Intermediate Status:
% 267.09/267.53 Generated: 799001
% 267.09/267.53 Kept: 195076
% 267.09/267.53 Inuse: 2056
% 267.09/267.53 Deleted: 3677
% 267.09/267.53 Deletedinuse: 100
% 267.09/267.53
% 267.09/267.53 Resimplifying inuse:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53
% 267.09/267.53 Intermediate Status:
% 267.09/267.53 Generated: 806728
% 267.09/267.53 Kept: 197963
% 267.09/267.53 Inuse: 2061
% 267.09/267.53 Deleted: 3677
% 267.09/267.53 Deletedinuse: 100
% 267.09/267.53
% 267.09/267.53 Resimplifying inuse:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53 Resimplifying inuse:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53
% 267.09/267.53 Intermediate Status:
% 267.09/267.53 Generated: 814873
% 267.09/267.53 Kept: 200166
% 267.09/267.53 Inuse: 2095
% 267.09/267.53 Deleted: 3678
% 267.09/267.53 Deletedinuse: 100
% 267.09/267.53
% 267.09/267.53 Resimplifying inuse:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53 Resimplifying inuse:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53
% 267.09/267.53 Intermediate Status:
% 267.09/267.53 Generated: 823533
% 267.09/267.53 Kept: 202173
% 267.09/267.53 Inuse: 2114
% 267.09/267.53 Deleted: 3681
% 267.09/267.53 Deletedinuse: 102
% 267.09/267.53
% 267.09/267.53 Resimplifying inuse:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53 Resimplifying clauses:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53
% 267.09/267.53 Intermediate Status:
% 267.09/267.53 Generated: 839806
% 267.09/267.53 Kept: 208051
% 267.09/267.53 Inuse: 2129
% 267.09/267.53 Deleted: 4005
% 267.09/267.53 Deletedinuse: 102
% 267.09/267.53
% 267.09/267.53 Resimplifying inuse:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53 Resimplifying inuse:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53
% 267.09/267.53 Intermediate Status:
% 267.09/267.53 Generated: 848145
% 267.09/267.53 Kept: 210092
% 267.09/267.53 Inuse: 2153
% 267.09/267.53 Deleted: 4005
% 267.09/267.53 Deletedinuse: 102
% 267.09/267.53
% 267.09/267.53 Resimplifying inuse:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53 Resimplifying inuse:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53
% 267.09/267.53 Intermediate Status:
% 267.09/267.53 Generated: 855594
% 267.09/267.53 Kept: 212125
% 267.09/267.53 Inuse: 2167
% 267.09/267.53 Deleted: 4005
% 267.09/267.53 Deletedinuse: 102
% 267.09/267.53
% 267.09/267.53 Resimplifying inuse:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53 Resimplifying inuse:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53
% 267.09/267.53 Intermediate Status:
% 267.09/267.53 Generated: 861841
% 267.09/267.53 Kept: 214129
% 267.09/267.53 Inuse: 2179
% 267.09/267.53 Deleted: 4005
% 267.09/267.53 Deletedinuse: 102
% 267.09/267.53
% 267.09/267.53 Resimplifying inuse:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53 Resimplifying inuse:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53
% 267.09/267.53 Intermediate Status:
% 267.09/267.53 Generated: 867285
% 267.09/267.53 Kept: 216405
% 267.09/267.53 Inuse: 2199
% 267.09/267.53 Deleted: 4005
% 267.09/267.53 Deletedinuse: 102
% 267.09/267.53
% 267.09/267.53 Resimplifying inuse:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53 Resimplifying inuse:
% 267.09/267.53 Done
% 267.09/267.53
% 267.09/267.53
% 267.09/267.53 Intermediate Status:
% 267.09/267.53 Generated: 876281
% 267.09/267.53 Kept: 218761
% 267.09/267.53 Inuse: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------