%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW272+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 23:21:44 EDT 2022
% Result : Theorem 19.99s 20.35s
% Output : Refutation 19.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW272+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Mon Jun 6 06:40:07 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.96/1.60 *** allocated 10000 integers for termspace/termends
% 0.96/1.60 *** allocated 10000 integers for clauses
% 0.96/1.60 *** allocated 10000 integers for justifications
% 0.96/1.60 *** allocated 15000 integers for termspace/termends
% 0.96/1.60 *** allocated 22500 integers for termspace/termends
% 0.96/1.60 *** allocated 33750 integers for termspace/termends
% 0.96/1.60 Bliksem 1.12
% 0.96/1.60
% 0.96/1.60
% 0.96/1.60 Automatic Strategy Selection
% 0.96/1.60
% 0.96/1.60 *** allocated 50625 integers for termspace/termends
% 0.96/1.60 *** allocated 75937 integers for termspace/termends
% 0.96/1.60 *** allocated 113905 integers for termspace/termends
% 0.96/1.60
% 0.96/1.60 Clauses:
% 0.96/1.60
% 0.96/1.60 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.96/1.60 { ! v_pa____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.96/1.60 tc_Complex_Ocomplex ) ) }.
% 0.96/1.60 { ! v_qa____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.96/1.60 tc_Complex_Ocomplex ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.96/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), !
% 0.96/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Polynomial_Opoly( X ) ),
% 0.96/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! v_n = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.96/1.60 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.96/1.60 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q ), X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.96/1.60 { ! v_na____ = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.96/1.60 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_qa____ ), X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.96/1.60 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_a____ ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 0.96/1.60 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol2( X
% 0.96/1.60 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol2( X, Y, Z ) ), Z = Y
% 0.96/1.60 }.
% 0.96/1.60 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.96/1.60 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.96/1.60 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.96/1.60 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 0.96/1.60 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 0.96/1.60 c_Polynomial_Ocoeff( X, Y ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.60 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.60 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.96/1.60 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.96/1.60 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.96/1.60 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.60 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.96/1.60 { c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) = v_n }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.60 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), !
% 0.96/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ),
% 0.96/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { c_Polynomial_Odegree( tc_Complex_Ocomplex, v_pa____ ) = v_na____ }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.96/1.60 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.96/1.60 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, T, Z ) ), Y ) ),
% 0.96/1.60 alpha1( X, Y, T ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, T, Z ) ), Y ) ),
% 0.96/1.60 alpha13( X, Y, Z, T ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! alpha1( X, Y, T ), ! alpha13( X, Y, Z, T )
% 0.96/1.60 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.96/1.60 , c_Polynomial_Osmult( X, T, Z ) ), Y ) ) }.
% 0.96/1.60 { ! alpha13( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.96/1.60 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.96/1.60 ) ) }.
% 0.96/1.60 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha13( X, Y, Z, T ) }.
% 0.96/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.96/1.60 , Z ), Y ) ), alpha13( X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha1( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { Z = c_Groups_Ozero__class_Ozero( X ), alpha1( X, Y, Z ) }.
% 0.96/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha1( X
% 0.96/1.60 , Y, Z ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.60 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.96/1.60 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.60 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.60 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.60 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.96/1.60 c_Polynomial_Odegree( X, Y ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.96/1.60 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.96/1.60 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.96/1.60 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.96/1.60 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.60 c_Polynomial_Odegree( X, Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), ! hBOOL
% 0.96/1.60 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Y ),
% 0.96/1.60 Z ) ), Z = Y }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 0.96/1.60 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult
% 0.96/1.60 ( X, T, Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), hBOOL(
% 0.96/1.60 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ),
% 0.96/1.60 c_Polynomial_Osmult( X, T, Y ) ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.96/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) =
% 0.96/1.60 c_Polynomial_Odegree( X, Z ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.60 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.60 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ) ) = Z }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Osmult( X, Z, Y ) ) ), Z
% 0.96/1.60 = c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), T = c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.96/1.60 X ) ), c_Polynomial_Osmult( X, T, Z ) ), Y ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 0.96/1.60 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 0.96/1.60 c_Polynomial_Osmult( X, Y, Z ) ) ), hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Z ) ) }.
% 0.96/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 0.96/1.60 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 0.96/1.60 Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.96/1.60 X ) ), T ), c_Polynomial_Osmult( X, Y, Z ) ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 0.96/1.60 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.96/1.60 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.96/1.60 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.96/1.60 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.96/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.96/1.60 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! v_qa____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.96/1.60 tc_Complex_Ocomplex ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), v_pa____ ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.96/1.60 ), v_qa____ ), v_na____ ) ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) )
% 0.96/1.60 }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Oorder(
% 0.96/1.60 tc_Complex_Ocomplex, X, v_pa____ ), v_na____ ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) )
% 0.96/1.60 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 0.96/1.60 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.60 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.96/1.60 }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 0.96/1.60 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ),
% 0.96/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ),
% 0.96/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 0.96/1.60 c_Polynomial_Odegree( X, Y ) ) }.
% 0.96/1.60 { v_pa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 0.96/1.60 ( tc_Complex_Ocomplex ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.96/1.60 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 0.96/1.60 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 0.96/1.60 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.96/1.60 ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) ) )
% 0.96/1.60 , v_s____ ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, v_na____ ), ! hAPP(
% 0.96/1.60 c_Polynomial_Opoly( tc_Complex_Ocomplex, Z ), skol3( T, Z ) ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.96/1.60 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = X, X =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), Y
% 0.96/1.60 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.96/1.60 tc_Complex_Ocomplex ) ), Z ), X ) ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, v_na____ ), hAPP(
% 0.96/1.60 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), skol3( Y, Z ) ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.96/1.60 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = X, X =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), Y
% 0.96/1.60 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.96/1.60 tc_Complex_Ocomplex ) ), Z ), X ) ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.96/1.60 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.96/1.60 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.96/1.60 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.96/1.60 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Ocoeff( X, c_Polynomial_OpCons( X
% 0.96/1.60 , Z, Y ) ) = c_Nat_Onat_Onat__case( X, Z, c_Polynomial_Ocoeff( X, Y ) ) }
% 0.96/1.60 .
% 0.96/1.60 { v_qa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 0.96/1.60 ( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 0.96/1.60 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.96/1.60 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.96/1.60 tc_Complex_Ocomplex ) ) ) ) ), v_r____ ) }.
% 0.96/1.60 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.96/1.60 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 0.96/1.60 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.96/1.60 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.96/1.60 tc_Complex_Ocomplex ) ) ) ) ), v_qa____ ) ) }.
% 0.96/1.60 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.96/1.60 tc_Complex_Ocomplex ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.96/1.60 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 0.96/1.60 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 0.96/1.60 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.96/1.60 ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) ) )
% 0.96/1.60 , v_pa____ ) ) }.
% 0.96/1.60 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.96/1.60 tc_Complex_Ocomplex ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.96/1.60 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 0.96/1.60 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 0.96/1.60 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.96/1.60 ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____,
% 0.96/1.60 v_pa____ ) ) ) ), v_pa____ ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.96/1.60 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha2( X, Y
% 0.96/1.60 , Z ), alpha14( X, Y, Z ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha14( X, Y, Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.60 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.96/1.60 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ), alpha14( X, Y, Z ) }.
% 0.96/1.60 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.96/1.60 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), alpha2( X, Y, Z ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( X ) ), alpha3( X, Y, Z ), alpha15( X, Y, Z ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( X ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha15( X, Y, Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( X ) ) }.
% 0.96/1.60 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.96/1.60 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( X ), Y ), alpha15( X, Y, Z ) }.
% 0.96/1.60 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.96/1.60 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ), alpha3( X, Y, Z ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha4( X, Y, Z, T ),
% 0.96/1.60 alpha16( X, Y, Z, T ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z, T ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha16( X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.96/1.60 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.60 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha4( X, Y, Z, T ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha5( X, Y, Z, T ),
% 0.96/1.60 alpha17( X, Y, Z, T ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z, T ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha17( X, Y, Z, T ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.60 { ! alpha17( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! alpha17( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha17( X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.96/1.60 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.96/1.60 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha5( X, Y, Z, T ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.96/1.60 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.96/1.60 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( X ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( X ) ) }.
% 0.96/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.96/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.96/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( X ) ) }.
% 0.96/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( X ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.60 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.96/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Oordered__semiring( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.60 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.60 { ! class_Rings_Oordered__semiring( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.60 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.60 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.96/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.96/1.60 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.96/1.60 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.60 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.96/1.60 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.60 { ! class_Rings_Oordered__semiring( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.60 { ! class_Rings_Oordered__semiring( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.60 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.60 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.60 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.60 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.96/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.60 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.96/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( X ) ) }.
% 0.96/1.60 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.60 ) ), Y ) }.
% 0.96/1.60 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.96/1.60 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.96/1.60 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.96/1.60 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.96/1.60 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.60 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.60 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.96/1.60 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.96/1.60 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, Y, Z ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.60 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.96/1.60 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.60 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.60 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.96/1.60 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.60 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.60 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.60 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.96/1.60 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Y ), Z ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.60 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Z ), Y ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.60 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.96/1.60 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.60 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.60 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.60 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.60 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.96/1.60 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.96/1.60 = Y }.
% 0.96/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.96/1.60 = Y }.
% 0.96/1.60 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.60 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.96/1.60 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.96/1.60 = Y }.
% 0.96/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.96/1.60 = Y }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.60 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , Y ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.60 , Y ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.96/1.60 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.60 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.60 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Y ), Y ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.96/1.60 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 0.96/1.60 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 0.96/1.60 X, Z ), Y ) ) }.
% 0.96/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.96/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.96/1.60 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.96/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.96/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.96/1.60 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 0.96/1.60 ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.96/1.60 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.96/1.60 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.96/1.60 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.96/1.60 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.96/1.60 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.60 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.96/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.96/1.60 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.96/1.60 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.96/1.60 ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.96/1.60 ) ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ouminus__class_Ouminus( X, Z ) )
% 0.96/1.60 , Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ouminus__class_Ouminus( X, Z ) )
% 0.96/1.60 , Y ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.96/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.96/1.60 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), U ), T ) ), hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T
% 0.96/1.60 ) ) ) }.
% 0.96/1.60 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), Y ), T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z
% 0.96/1.60 ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), Z ), T ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 0.96/1.60 ), Z ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), T ), Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 0.96/1.60 ), Z ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), c_Groups_Oone__class_Oone( X ) ), Y ) ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Oorder( X, Z, Y ) ) ), Y )
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.96/1.60 Y ) ) ) ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.96/1.60 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.96/1.60 Y ) ) ) ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.60 = Y }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.96/1.60 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( X ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.60 , Y ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 = Y }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.96/1.60 , c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Z, Y ) ), c_Nat_OSuc(
% 0.96/1.60 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.60 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.96/1.60 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.96/1.60 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.96/1.60 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.60 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), T =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.96/1.60 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.60 X ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.60 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), T ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.96/1.60 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.60 X ), T ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Oorder( X, Z, Y ) ) ), Y )
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 0.96/1.60 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 0.96/1.60 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.96/1.60 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.96/1.60 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.96/1.60 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 0.96/1.60 ( X ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.96/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), ! hAPP(
% 0.96/1.60 c_Polynomial_Ocoeff( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 0.96/1.60 , Y ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.60 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 0.96/1.60 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.96/1.60 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 0.96/1.60 Y ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.60 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.96/1.60 , Y ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.60 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 0.96/1.60 ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.96/1.60 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) )
% 0.96/1.60 , c_Polynomial_Odegree( X, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.96/1.60 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.96/1.60 , c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Z, Y ) ), Y ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons
% 0.96/1.60 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.96/1.60 , Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X, Z,
% 0.96/1.60 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ),
% 0.96/1.60 hAPP( c_Polynomial_Opoly( X, Y ), c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.96/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.96/1.60 ) ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.96/1.60 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.60 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 0.96/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.96/1.60 tc_Nat_Onat, Y, c_Polynomial_Odegree( X, Z ) ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 0.96/1.60 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), Y ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 0.96/1.60 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), Z ), Y ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.96/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.96/1.60 }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.96/1.60 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 0.96/1.60 ) }.
% 0.96/1.60 { v_pa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 0.96/1.60 ( tc_Complex_Ocomplex ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.96/1.60 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 0.96/1.60 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 0.96/1.60 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.96/1.60 ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) ) )
% 0.96/1.60 , skol4 ) }.
% 0.96/1.60 { v_qa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 0.96/1.60 ( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 0.96/1.60 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.96/1.60 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.96/1.60 tc_Complex_Ocomplex ) ) ) ) ), skol5 ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.96/1.61 X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.61 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), hBOOL( hAPP
% 0.96/1.61 ( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.96/1.61 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.96/1.61 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), X ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.96/1.61 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.61 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.96/1.61 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.61 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.96/1.61 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.96/1.61 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.61 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.96/1.61 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.96/1.61 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.61 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.96/1.61 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.61 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.96/1.61 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.61 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.96/1.61 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.61 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.96/1.61 ), Z ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.61 , ! X = Z, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.96/1.61 Z ), Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.61 , ! X = Y }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.61 , ! Y = X }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.61 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.96/1.61 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.61 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.96/1.61 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.61 , ! Y = X }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.96/1.61 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.96/1.61 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.96/1.61 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.96/1.61 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.96/1.61 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.96/1.61 ), X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.96/1.61 ), Z ) ) }.
% 0.96/1.61 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.96/1.61 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.96/1.61 ), X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.96/1.61 Z ), Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.96/1.61 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.96/1.61 ), Y = X }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.96/1.61 ), Y = X }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.96/1.61 ), Z ) ) }.
% 0.96/1.61 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.96/1.61 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.96/1.61 ), Z ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.96/1.61 , X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.96/1.61 ), Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , Y = X }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.96/1.61 ), Y = X }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.96/1.61 ), X = Y }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , ! X = Y, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.96/1.61 ), Y ) ) }.
% 0.96/1.61 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.96/1.61 , X ) ) }.
% 0.96/1.61 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.96/1.61 , X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.96/1.61 , X ) ) }.
% 0.96/1.61 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.96/1.61 , X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.96/1.61 ), Y ) ) }.
% 0.96/1.61 { ! alpha6( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.61 tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { ! alpha6( X, Y ), ! Y = X }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , Y = X, alpha6( X, Y ) }.
% 0.96/1.61 { ! alpha6( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.61 tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { ! alpha6( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.61 tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.61 , alpha6( X, Y ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , alpha7( X, Y ), Y = X }.
% 0.96/1.61 { ! alpha7( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.61 tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.96/1.61 , X ) ) }.
% 0.96/1.61 { ! alpha7( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.61 tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { ! alpha7( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.61 tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.61 , alpha7( X, Y ) }.
% 0.96/1.61 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.96/1.61 , X ) ) }.
% 0.96/1.61 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X )
% 0.96/1.61 , Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.96/1.61 ), Y = X }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X =
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.61 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Nat_Onat ) ) ) }.
% 0.96/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.96/1.61 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.96/1.61 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.96/1.61 .
% 0.96/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.96/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.96/1.61 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.96/1.61 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.96/1.61 .
% 0.96/1.61 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.96/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.96/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.96/1.61 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.61 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.96/1.61 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.61 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.61 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.96/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Nat_Onat ) ) = Y }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.96/1.61 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.96/1.61 ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.61 Y ), X ) ), X ) ), Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.96/1.61 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.61 X ), Y ) ), X ) ), Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.96/1.61 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X ) ) }.
% 0.96/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.96/1.61 c_Polynomial_Odegree( X, Y ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.96/1.61 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.96/1.61 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.96/1.61 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.96/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.96/1.61 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.96/1.61 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.96/1.61 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.96/1.61 ), X ) ) }.
% 0.96/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.96/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.96/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.96/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), Z ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.61 tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.96/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), Z ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.96/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.96/1.61 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.96/1.61 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.61 Y ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.96/1.61 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.96/1.61 ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.96/1.61 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.96/1.61 ), X ) ) }.
% 0.96/1.61 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.96/1.61 ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.96/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.96/1.61 ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.96/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.96/1.61 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.96/1.61 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.96/1.61 { ! c_Nat_OSuc( X ) = X }.
% 0.96/1.61 { ! X = c_Nat_OSuc( X ) }.
% 0.96/1.61 { alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.96/1.61 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.96/1.61 { alpha23( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.96/1.61 ( X, Y ), Z ) ) }.
% 0.96/1.61 { ! alpha23( X, Y, Z ), alpha25( X, Y, Z ), Z = Y }.
% 0.96/1.61 { ! alpha23( X, Y, Z ), alpha25( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! alpha25( X, Y, Z ), alpha23( X, Y, Z ) }.
% 0.96/1.61 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha23( X, Y, Z ) }.
% 0.96/1.61 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.96/1.61 }.
% 0.96/1.61 { ! alpha25( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.96/1.61 X, Y ), Z ) ), alpha25( X, Y, Z ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.96/1.61 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.96/1.61 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.96/1.61 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Orderings_Oord__class_Oless__eq
% 0.96/1.61 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.61 c_Polynomial_Odegree( X, Z ) ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.96/1.61 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Opcompose( X, Z, Y )
% 0.96/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.61 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( X ) }.
% 0.96/1.61 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.96/1.61 = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.61 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.96/1.61 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.96/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.96/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.96/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hBOOL(
% 0.96/1.61 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.96/1.61 .
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.96/1.61 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.96/1.61 X ), Z ), T ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T )
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.96/1.61 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.96/1.61 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.96/1.61 .
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.96/1.61 .
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.96/1.61 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.96/1.61 X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.61 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.96/1.61 }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.96/1.61 ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.96/1.61 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.96/1.61 }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.96/1.61 c_Nat_OSuc( X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.96/1.61 ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.61 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.96/1.61 , c_Nat_OSuc( X ) ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.96/1.61 .
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { hAPP( c_Nat_Onat_Onat__case( Z, Y, X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ) ) = Y }.
% 0.96/1.61 { hAPP( c_Nat_Onat_Onat__case( T, Z, Y ), c_Nat_OSuc( X ) ) = hAPP( Y, X )
% 0.96/1.61 }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.96/1.61 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.96/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.96/1.61 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.96/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.96/1.61 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ) }.
% 0.96/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.96/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.96/1.61 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.96/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.96/1.61 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.61 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.96/1.61 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.96/1.61 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.96/1.61 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.96/1.61 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.96/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 0.96/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.61 { ! alpha8( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.96/1.61 c_Nat_OSuc( X ) ) }.
% 0.96/1.61 { ! alpha8( X, Y ), Y = c_Nat_OSuc( skol6( Z, Y ) ) }.
% 0.96/1.61 { ! alpha8( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol6( X, Y
% 0.96/1.61 ), X ) }.
% 0.96/1.61 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.96/1.61 ), alpha8( X, Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol7( X ) ) }.
% 0.96/1.61 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP
% 0.96/1.61 ( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.96/1.61 ( X ), T ), Z ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y
% 0.96/1.61 ) ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ), hBOOL( hAPP( hAPP
% 0.96/1.61 ( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.96/1.61 ( X ), Z ), U ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T
% 0.96/1.61 ) ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.96/1.61 X ), T ), Z ) ), Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.96/1.61 , U, Z ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), U ) ), Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.96/1.61 .
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.96/1.61 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.61 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 X ), Y ), Z = Y }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.61 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.96/1.61 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.61 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.61 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.96/1.61 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.61 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.96/1.61 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.96/1.61 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.96/1.61 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.96/1.61 c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.96/1.61 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.96/1.61 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.96/1.61 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.96/1.61 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.96/1.61 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.96/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.96/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.96/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.96/1.61 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.96/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.96/1.61 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.61 X ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 0.96/1.61 , Y ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.96/1.61 ), Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.61 tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.61 X ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 0.96/1.61 , Y ) ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.61 tc_Nat_Onat ), Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.96/1.61 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.61 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.61 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.96/1.61 , Y ), X ) }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.96/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.96/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Nat_Onat ) }.
% 0.96/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Nat_Onat ) }.
% 0.96/1.61 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.96/1.61 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.96/1.61 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.96/1.61 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.96/1.61 .
% 0.96/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ), hBOOL( hAPP(
% 0.96/1.61 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.96/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 0.96/1.61 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ), Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Nat_Onat ) ) = Y }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.96/1.61 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.96/1.61 = Y }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.96/1.61 = Y }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.61 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.61 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.61 tc_Nat_Onat ), X ), Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.96/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.96/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.96/1.61 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), Y ) }.
% 0.96/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.96/1.61 ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), Z =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.96/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.96/1.61 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.96/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.96/1.61 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ), Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.96/1.61 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.96/1.61 , Y ) }.
% 0.96/1.61 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.96/1.61 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.96/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.96/1.61 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.61 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.61 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.61 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.96/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.61 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.96/1.61 ), U = Z, T = Y }.
% 0.96/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.61 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.61 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.96/1.61 ) ), Z ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.61 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.61 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.61 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.96/1.61 ), ! U = T }.
% 0.96/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.61 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.96/1.61 ), ! Z = Y }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.96/1.61 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.96/1.61 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.96/1.61 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.96/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.61 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.61 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.96/1.61 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.96/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.96/1.61 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.96/1.61 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.96/1.61 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.96/1.61 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.61 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.61 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, Z, Y ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, Z, Y ) }.
% 0.96/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.61 , T ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.61 , T, Y ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.61 , Y, T ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, Z, Y ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.61 , T, Y ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, T, Y ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.61 , Y, Z ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.61 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.96/1.61 ) ), T ), Y ) }.
% 0.96/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 Z, Y ) ) = Y }.
% 0.96/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.96/1.61 Y ) ) = Y }.
% 0.96/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.96/1.61 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.96/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.96/1.61 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X, Y, T
% 0.96/1.61 ) ) ) }.
% 0.96/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.96/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.96/1.61 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.96/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 T, Y ), Z = Y }.
% 0.96/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 T, Y ) }.
% 0.96/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 Y, Z ), T = Y }.
% 0.96/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 Y, Z ) }.
% 0.96/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 T, Y ), Z = Y }.
% 0.96/1.61 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 T, Y ), Z = Y }.
% 0.96/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 Y, T ), Z = Y }.
% 0.96/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.96/1.61 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.96/1.61 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 0.96/1.61 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.96/1.61 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.96/1.61 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.96/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.96/1.61 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.96/1.61 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.96/1.61 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 0.96/1.61 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.96/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.96/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.96/1.61 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 Z, Y ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 Y, Z ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.96/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.96/1.61 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.96/1.61 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.61 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.96/1.61 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.61 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.61 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.96/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.96/1.61 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.96/1.61 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.96/1.61 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.61 , Y, T ) ) }.
% 0.96/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.61 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.96/1.61 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.61 Z ) = Y }.
% 0.96/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.61 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.96/1.61 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.96/1.61 ( X, Y ) }.
% 0.96/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 X ) }.
% 0.96/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.96/1.61 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.96/1.61 ( X, Z ) }.
% 0.96/1.61 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.61 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.61 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.96/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.96/1.61 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.61 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.61 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.96/1.61 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.61 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.96/1.61 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.96/1.61 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.61 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.96/1.61 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.96/1.61 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.61 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.96/1.61 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.96/1.61 { ! class_Groups_Ocomm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.96/1.61 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 0.96/1.61 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.96/1.61 , Y ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.61 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.61 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.61 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.61 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.61 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.61 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.96/1.61 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.96/1.61 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.96/1.61 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.61 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.96/1.61 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.96/1.61 hAPP( Y, U ) ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.61 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.61 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.61 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.61 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.61 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.96/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.96/1.61 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.96/1.61 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.61 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.61 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.61 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.96/1.61 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.96/1.61 hAPP( Y, U ) ) }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.96/1.61 ( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.96/1.61 ( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.61 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.61 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.96/1.61 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.96/1.61 hAPP( Y, U ) ) }.
% 0.96/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.96/1.61 ( Z, skol8( X, Y, Z ) ), hAPP( Y, skol8( X, Y, Z ) ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.61 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.61 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.61 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.61 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.61 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.96/1.61 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.96/1.61 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.96/1.61 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.61 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.61 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.61 , ! Y = Z }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.61 , ! Z = Y }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.61 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.61 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.61 , ! Z = Y }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.61 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.61 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.61 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.61 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.61 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.61 Y ), ! Z = Y }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.61 Z ), ! Z = Y }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.61 Y ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.61 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.96/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.96/1.61 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.96/1.61 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.96/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.96/1.61 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 0.96/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 0.96/1.61 c_Polynomial_OpCons( X, T,
% 0.96/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.96/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.96/1.61 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.96/1.61 ), Y ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.96/1.61 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.96/1.61 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.96/1.61 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 0.96/1.61 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.96/1.61 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 0.96/1.61 }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.96/1.61 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 0.96/1.61 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 0.96/1.61 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 0.96/1.61 , Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.96/1.61 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.96/1.61 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.96/1.61 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.96/1.61 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.61 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.61 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.61 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.61 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.61 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.61 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.61 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.61 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.61 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.61 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.61 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.61 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.61 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.61 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.61 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.61 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.61 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.61 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.96/1.61 ( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.61 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.61 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.61 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.61 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.61 , ! Z = Y }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.61 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.61 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.61 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.61 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.61 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.61 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.96/1.61 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.96/1.61 hAPP( Z, skol9( U, W, Z ) ) ) }.
% 0.96/1.61 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.96/1.61 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.96/1.61 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, skol9( X, Y, Z ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) ) ) }.
% 0.96/1.61 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.96/1.61 hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.61 , T, c_Groups_Ozero__class_Ozero( X ) ) ) ), ! hBOOL( hAPP( Z, T ) ),
% 0.96/1.61 hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.96/1.61 skol21( X, Y, Z ) ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ) }.
% 0.96/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.96/1.61 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.96/1.61 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 0.96/1.61 }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.96/1.61 , alpha21( X, Y, Z, T ) }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha21( X, Y, Z, T ),
% 0.96/1.61 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 0.96/1.61 { ! alpha21( X, Y, Z, T ), alpha9( X, Z, T ) }.
% 0.96/1.61 { ! alpha21( X, Y, Z, T ), alpha18( X, Y, T ) }.
% 0.96/1.61 { ! alpha9( X, Z, T ), ! alpha18( X, Y, T ), alpha21( X, Y, Z, T ) }.
% 0.96/1.61 { ! alpha18( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), alpha22( X, Y, Z ) }.
% 0.96/1.61 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha18( X
% 0.96/1.61 , Y, Z ) }.
% 0.96/1.61 { ! alpha22( X, Y, Z ), alpha18( X, Y, Z ) }.
% 0.96/1.61 { ! alpha22( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 0.96/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha22( X
% 0.96/1.61 , Y, Z ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 0.96/1.61 ), c_Polynomial_Odegree( X, Z ) ), alpha22( X, Y, Z ) }.
% 0.96/1.61 { ! alpha9( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha9( X, Y
% 0.96/1.61 , Z ) }.
% 0.96/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha9( X
% 0.96/1.61 , Y, Z ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ) ), hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.96/1.61 , Z ), X ) ), T ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.61 tc_Int_Oint ), Y ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ) )
% 0.96/1.61 }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ), hBOOL( hAPP
% 0.96/1.61 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ) }.
% 0.96/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.96/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), X ) = X }.
% 0.96/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ) ) = X }.
% 0.96/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.96/1.61 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.96/1.61 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.96/1.61 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.96/1.61 , X ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ), hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol10( X, Y ) ) }.
% 0.96/1.61 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.96/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.96/1.61 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.96/1.61 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.96/1.61 }.
% 0.96/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.96/1.61 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.96/1.61 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.96/1.61 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.96/1.61 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.96/1.61 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.96/1.61 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.96/1.61 , c_Polynomial_Opdivmod__rel( X, c_Polynomial_Osmult( X, W, U ), T,
% 0.96/1.61 c_Polynomial_Osmult( X, W, Z ), c_Polynomial_Osmult( X, W, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Z, Y ) ) }.
% 0.96/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.96/1.61 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha10( X, Y ),
% 0.96/1.61 alpha19( X, Y ) }.
% 0.96/1.61 { ! alpha10( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.96/1.61 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! alpha19( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.96/1.61 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! alpha19( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! alpha19( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha19( X, Y ) }.
% 0.96/1.61 { ! alpha10( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! alpha10( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha10( X, Y ) }.
% 0.96/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha11( X, Y ), alpha20( X
% 0.96/1.61 , Y ) }.
% 0.96/1.61 { ! alpha11( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.96/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! alpha20( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.96/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! alpha20( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! alpha20( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha20( X, Y ) }.
% 0.96/1.61 { ! alpha11( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! alpha11( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha11( X, Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol11( X, Y ) ) ) }.
% 0.96/1.61 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.96/1.61 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.96/1.61 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.96/1.61 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.96/1.61 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 0.96/1.61 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.96/1.61 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ),
% 0.96/1.61 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 0.96/1.61 c_Polynomial_Odegree( X, Z ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.96/1.61 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.96/1.61 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.96/1.61 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), ! hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP( hAPP
% 0.96/1.61 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ), X = Y }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.96/1.61 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.96/1.61 , ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) ), hBOOL( hAPP(
% 0.96/1.61 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ), hBOOL( hAPP( hAPP
% 0.96/1.61 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), Z =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 0.96/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 0.96/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ), hBOOL( hAPP(
% 0.96/1.61 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.96/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.96/1.61 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.96/1.61 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.96/1.61 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.61 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.96/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.96/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.96/1.61 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.61 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.96/1.61 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.96/1.61 alpha12( X, Y, Z ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.96/1.61 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! alpha12( X, Y, Z ),
% 0.96/1.61 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.96/1.61 { ! alpha12( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.61 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.96/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.96/1.61 alpha12( X, Y, Z ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.96/1.61 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.96/1.61 }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Int_Oint ) ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.96/1.61 = X }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Int_Oint ) ) ) }.
% 0.96/1.61 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Int_Oint ) ) ) }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.96/1.61 }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Int_Oint ) ), X ) }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Int_Oint ) ), X ) }.
% 0.96/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.96/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.96/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.96/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ) ) = X }.
% 0.96/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ), X ) = X }.
% 0.96/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.96/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.96/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.96/1.61 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.96/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.96/1.61 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.96/1.61 .
% 0.96/1.61 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.96/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.96/1.61 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.61 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.96/1.61 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.96/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.61 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.61 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.96/1.61 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.96/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.96/1.61 ( tc_Int_Oint ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.96/1.61 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.96/1.61 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.96/1.61 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.96/1.61 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.61 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.61 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.61 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.61 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.96/1.61 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.96/1.61 ( tc_Int_Oint ), Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.96/1.61 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.96/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.96/1.61 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.96/1.61 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.96/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.96/1.61 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.96/1.61 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.61 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ) ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Int_Oint ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Int_Oint, X, Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol12( X, Y ) ) }.
% 0.96/1.61 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.61 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.96/1.61 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.96/1.61 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.96/1.61 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.96/1.61 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.96/1.61 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.96/1.61 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.96/1.61 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.96/1.61 ( X, Y ), Z = Y }.
% 0.96/1.61 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.96/1.61 ( X, Y ) }.
% 0.96/1.61 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.61 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.61 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.61 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.61 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.96/1.61 , skol13( T, U, Z ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Polynomial_Odegree( X, Y ), Z ) }.
% 0.96/1.61 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ), skol13( X
% 0.96/1.61 , Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.96/1.61 Y ), Z ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol14( Z, Y ) ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.96/1.61 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Int_Oint, skol14( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.61 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.96/1.61 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 0.96/1.61 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.96/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.96/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.96/1.61 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.96/1.61 .
% 0.96/1.61 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.96/1.61 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol15( Z, Y
% 0.96/1.61 ), Y ) }.
% 0.96/1.61 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.96/1.61 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.96/1.61 skol15( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.96/1.61 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.96/1.61 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.96/1.61 , skol15( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.61 { ! class_Fields_Ofield( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) ), Z ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Fields_Ofield( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) ), Y ) ) }
% 0.96/1.62 .
% 0.96/1.62 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.96/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 0.96/1.62 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z,
% 0.96/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.96/1.62 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.96/1.62 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 0.96/1.62 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 0.96/1.62 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 0.96/1.62 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.96/1.62 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.96/1.62 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Opoly__gcd( X, Z, Y ) ) )
% 0.96/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.96/1.62 , T ), Z ) ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.96/1.62 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Opoly__gcd( X, Z, Y ) ) )
% 0.96/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.96/1.62 , T ), Y ) ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.96/1.62 ( tc_Polynomial_Opoly( X ) ), T ), Z ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Y ) ), hBOOL(
% 0.96/1.62 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 0.96/1.62 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.96/1.62 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), T ) ), hBOOL(
% 0.96/1.62 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ),
% 0.96/1.62 c_Polynomial_Opoly__gcd( X, Y, T ) ) ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.96/1.62 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.96/1.62 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.96/1.62 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.62 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.96/1.62 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), alpha26( X, Y, Z, T ), ! Y =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.62 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.96/1.62 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), alpha26( X, Y, Z, T ), ! hAPP(
% 0.96/1.62 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.96/1.62 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 0.96/1.62 .
% 0.96/1.62 { ! alpha26( X, Y, Z, T ), alpha27( X, Y, Z, T ), alpha24( X, Y, T ) }.
% 0.96/1.62 { ! alpha26( X, Y, Z, T ), alpha27( X, Y, Z, T ), ! hAPP(
% 0.96/1.62 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.62 { ! alpha27( X, Y, Z, T ), alpha26( X, Y, Z, T ) }.
% 0.96/1.62 { ! alpha24( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.96/1.62 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.62 alpha26( X, Y, Z, T ) }.
% 0.96/1.62 { ! alpha27( X, Y, Z, T ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ), Z ), T ) ), alpha28( X, Y, Z, T ) }.
% 0.96/1.62 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ),
% 0.96/1.62 Z ), T ) ), alpha27( X, Y, Z, T ) }.
% 0.96/1.62 { ! alpha28( X, Y, Z, T ), alpha27( X, Y, Z, T ) }.
% 0.96/1.62 { ! alpha28( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ), skol16( X, Y, U, W ) ), Y ) ) }.
% 0.96/1.62 { ! alpha28( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ), skol16( X, Y, U, T ) ), T ) ) }.
% 0.96/1.62 { ! alpha28( X, Y, Z, T ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ), skol16( X, Y, Z, T ) ), Z ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.96/1.62 , U ), Y ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ), U ), T ) ), hBOOL( hAPP( hAPP(
% 0.96/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), U ), Z ) ), alpha28
% 0.96/1.62 ( X, Y, Z, T ) }.
% 0.96/1.62 { ! alpha24( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! alpha24( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha24( X, Y, Z
% 0.96/1.62 ) }.
% 0.96/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X, Z, Y ) =
% 0.96/1.62 c_Polynomial_OAbs__poly( X, c_Nat_Onat_Onat__case( X, Z,
% 0.96/1.62 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 0.96/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_OAbs__poly( X,
% 0.96/1.62 c_Polynomial_Ocoeff( X, Y ) ) = Y }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.62 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 0.96/1.62 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 0.96/1.62 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.62 Z, c_Polynomial_Odegree( X, Y ) ), c_Orderings_Oord__class_Oless(
% 0.96/1.62 tc_Nat_Onat, Z, skol17( T, U, Z ) ) }.
% 0.96/1.62 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.62 Z, c_Polynomial_Odegree( X, Y ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.62 skol17( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.62 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.62 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.62 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.62 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.62 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 0.96/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 0.96/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.62 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.96/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.96/1.62 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.96/1.62 ) ), Z ) }.
% 0.96/1.62 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.62 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.62 = Y }.
% 0.96/1.62 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.62 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( X ) }.
% 0.96/1.62 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 0.96/1.62 X, Y ) ) = Y }.
% 0.96/1.62 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.62 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.96/1.62 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.62 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.96/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.62 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.62 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.96/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.62 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 0.96/1.62 ) ), Y ) }.
% 0.96/1.62 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.96/1.62 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.96/1.62 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 0.96/1.62 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.62 , Y ) ) = Y }.
% 0.96/1.62 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.96/1.62 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.62 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 0.96/1.62 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 0.96/1.62 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.96/1.62 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.96/1.62 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 0.96/1.62 ) }.
% 0.96/1.62 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.96/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.96/1.62 c_Polynomial_Opdivmod__rel( X, W, U, T, Z ), c_Polynomial_Opdivmod__rel(
% 0.96/1.62 X, W, c_Polynomial_Osmult( X, Y, U ), c_Polynomial_Osmult( X,
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ), T ), Z ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.96/1.62 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.96/1.62 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.96/1.62 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.96/1.62 X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.62 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.96/1.62 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.62 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.62 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.96/1.62 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.62 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 0.96/1.62 , Y = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.62 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 0.96/1.62 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 0.96/1.62 = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.62 ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.96/1.62 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.62 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.62 ) ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.62 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.62 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.62 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.96/1.62 .
% 0.96/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.62 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.62 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.62 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.96/1.62 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( X ) ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.62 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.62 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.96/1.62 .
% 0.96/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.62 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.62 , Y ) ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.96/1.62 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.96/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.96/1.62 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.62 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.62 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.62 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.62 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.62 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 0.96/1.62 , Y ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.96/1.62 ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.96/1.62 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse
% 0.96/1.62 ( X, Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.96/1.62 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.62 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.62 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.62 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 0.96/1.62 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.96/1.62 ) ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.96/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.96/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.62 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.96/1.62 }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.62 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 0.96/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 0.96/1.62 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 0.96/1.62 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 0.96/1.62 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 0.96/1.62 c_Polynomial_Opoly__gcd( X, Z, c_Divides_Odiv__class_Omod(
% 0.96/1.62 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.62 skol18( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, skol18( X, T, U ),
% 0.96/1.62 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.62 , Y ) }.
% 0.96/1.62 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), skol18( X, Y, Z ) ), Z ), Y ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.62 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.96/1.62 ( X, c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Omod( X, Z
% 0.96/1.62 , Y ) ), Y ) }.
% 0.96/1.62 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.96/1.62 = c_Divides_Odiv__class_Omod( X, Y, Z ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.62 c_Groups_Ouminus__class_Ouminus( X, T ), Z ) = c_Divides_Odiv__class_Omod
% 0.96/1.62 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.96/1.62 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.96/1.62 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.96/1.62 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.96/1.62 ( X ), Z, Y ) ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.96/1.62 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.96/1.62 tc_Polynomial_Opoly( X ), Y ) ) = c_Divides_Odiv__class_Omod(
% 0.96/1.62 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T,
% 0.96/1.62 c_Polynomial_Osmult( X, Y, Z ) ) = c_Divides_Odiv__class_Omod(
% 0.96/1.62 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.96/1.62 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.96/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 0.96/1.62 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Omod(
% 0.96/1.62 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.96/1.62 , c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.62 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 0.96/1.62 X, Z, Y ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.62 c_Rings_Odvd__class_Odvd( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.96/1.62 ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), T ), Y ) ),
% 0.96/1.62 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), T ), Z ) ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.96/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, Y, T )
% 0.96/1.62 ) ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 0.96/1.62 , c_Divides_Odiv__class_Omod( X, T, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.96/1.62 ( X, T, Z ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.96/1.62 ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.96/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.96/1.62 ) ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 0.96/1.62 , Y, Z ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 0.96/1.62 , Y, Z ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 0.96/1.62 Z ) = c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.96/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.96/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.96/1.62 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.96/1.62 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.62 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.96/1.62 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.62 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.96/1.62 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.62 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 0.96/1.62 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 0.96/1.62 , Y ) ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.96/1.62 ), Z ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 0.96/1.62 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.96/1.62 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.96/1.62 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.96/1.62 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.62 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 0.96/1.62 ( X, Z, Y ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.96/1.62 ( X, Y, Z ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.96/1.62 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 0.96/1.62 , Y ) ), Y ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.96/1.62 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.96/1.62 ), Z ), Y ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.96/1.62 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.96/1.62 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.96/1.62 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.62 T, Z ), Y ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 0.96/1.62 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.62 T, Y ), Z ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.96/1.62 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.96/1.62 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.96/1.62 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 0.96/1.62 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 0.96/1.62 ), Z ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.96/1.62 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 0.96/1.62 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.96/1.62 c_Polynomial_Opoly__gcd( X, Y, c_Divides_Odiv__class_Omod(
% 0.96/1.62 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 0.96/1.62 tc_Polynomial_Opoly( X ), Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.62 c_Polynomial_Odegree( X, c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.96/1.62 ( X ), Z, Y ) ), c_Polynomial_Odegree( X, Y ) ) }.
% 0.96/1.62 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.96/1.62 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.62 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.96/1.62 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.96/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.96/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Omono( tc_Nat_Onat, X
% 0.96/1.62 , c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), ! hBOOL( hAPP( hAPP(
% 0.96/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), T ), Z ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.96/1.62 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.96/1.62 ( tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.96/1.62 ( tc_Int_Oint, Y ), X ) }.
% 0.96/1.62 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.96/1.62 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.96/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.96/1.62 ( tc_Int_Oint, Y, X ) ) }.
% 0.96/1.62 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.96/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.96/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.96/1.62 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) ) }
% 0.96/1.62 .
% 0.96/1.62 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.96/1.62 ( tc_Int_Oint, Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.62 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.96/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 0.96/1.62 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.62 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.96/1.62 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 0.96/1.62 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.96/1.62 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 0.96/1.62 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 0.96/1.62 , U ), Z ) }.
% 0.96/1.62 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.96/1.62 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.96/1.62 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 0.96/1.62 Y ) ), Y ) }.
% 0.96/1.62 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.96/1.62 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.96/1.62 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 0.96/1.62 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.96/1.62 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.96/1.62 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.96/1.62 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 0.96/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! hBOOL( hAPP( hAPP
% 0.96/1.62 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ), hBOOL( hAPP( hAPP
% 0.96/1.62 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.96/1.62 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), Z )
% 0.96/1.62 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) ) }.
% 0.96/1.62 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.96/1.62 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 0.96/1.62 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 0.96/1.62 }.
% 0.96/1.62 { ! c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.62 { c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.96/1.62 c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.62 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.96/1.62 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol19( X, Y ) ) }.
% 0.96/1.62 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 0.96/1.62 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.96/1.62 ( tc_Int_Oint, Y, X ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.96/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.96/1.62 tc_Nat_Onat, Y, X ), X ) }.
% 0.96/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.96/1.62 tc_Nat_Onat, Y, X ), X ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.96/1.62 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.62 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.62 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 0.96/1.62 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 0.96/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.62 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol20( X, Y ) ) }.
% 0.96/1.62 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 0.96/1.62 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), Y ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) =
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.96/1.62 tc_Nat_Onat, X, Y ), Y ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.96/1.62 tc_Int_Oint, X, Y ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 0.96/1.62 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 0.96/1.62 ), Y ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 0.96/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.62 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.62 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.96/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.96/1.62 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.62 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.96/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.62 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.62 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.96/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.62 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.96/1.62 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.62 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.96/1.62 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.96/1.62 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.96/1.62 hAPP( Z, Y ) ) }.
% 0.96/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.62 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.96/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.96/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.96/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.96/1.62 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.96/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.62 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.62 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.96/1.62 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.96/1.62 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.96/1.62 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.96/1.62 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.96/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.96/1.62 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 0.96/1.62 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.96/1.62 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 0.96/1.62 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.96/1.62 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.96/1.62 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.96/1.62 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.96/1.62 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.96/1.62 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.96/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.96/1.62 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 0.96/1.62 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.96/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.62 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.96/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.62 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.96/1.62 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) ) }.
% 0.96/1.62 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.96/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.96/1.62 T ) ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), ! hBOOL( hAPP(
% 0.96/1.62 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), hBOOL( hAPP( hAPP
% 0.96/1.62 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), ! hBOOL( hAPP(
% 0.96/1.62 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), hBOOL( hAPP( hAPP
% 0.96/1.62 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.62 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.96/1.62 ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.62 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.96/1.62 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.62 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.96/1.62 ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.96/1.62 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.96/1.62 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.62 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.62 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.96/1.62 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.62 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.96/1.62 Z ) ), U ), T ) = Y }.
% 0.96/1.62 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.96/1.62 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.62 ( X ), Z ), U ), Y ) }.
% 0.96/1.62 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.62 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.96/1.62 W ) ), U ), Y ) }.
% 0.96/1.62 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.62 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.62 ( X ), Z ), U ), Y ) }.
% 0.96/1.62 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.62 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.96/1.62 Z ) ), Y ) ) }.
% 0.96/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.62 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( X ) ) }.
% 0.96/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.96/1.62 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.96/1.62 , Z, Y ) }.
% 0.96/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.96/1.62 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.96/1.62 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.62 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.96/1.62 ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.62 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.96/1.62 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.96/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.96/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.62 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.96/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.62 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.96/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.96/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.96/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.62 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.96/1.62 ) }.
% 0.96/1.62 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.96/1.62 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.96/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.96/1.62 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.96/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.96/1.62 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.96/1.62 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.96/1.62 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.96/1.62 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.96/1.62 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.62 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.96/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.62 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.96/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.96/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.62 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.96/1.62 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.62 tc_Nat_Onat, Z, Y ), X ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.62 tc_Nat_Onat, Z, X ), Y ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.62 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.96/1.62 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.96/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.62 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.62 tc_Nat_Onat, Z, X ), Y ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.96/1.62 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.96/1.62 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.96/1.62 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.96/1.62 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.96/1.62 ( tc_fun( Y, X ) ) }.
% 0.96/1.62 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.96/1.62 ) ) }.
% 0.96/1.62 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.96/1.62 .
% 0.96/1.62 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.96/1.62 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.96/1.62 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.96/1.62 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.96/1.62 tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.96/1.62 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.96/1.62 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.96/1.62 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.96/1.62 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.96/1.62 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.96/1.62 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.96/1.62 { class_Power_Opower( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.96/1.62 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.96/1.62 tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.96/1.62 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.96/1.62 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.96/1.62 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.96/1.62 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.96/1.62 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.96/1.62 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.96/1.62 tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.96/1.62 { ! class_Rings_Oidom( X ),
% 0.96/1.62 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.62 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.96/1.62 ) ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.62 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.96/1.62 X ) ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.62 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.96/1.62 ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.62 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.96/1.62 }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.62 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.62 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.62 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.62 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.96/1.62 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.62 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.62 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.62 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.62 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.62 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.96/1.62 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.96/1.62 ( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.96/1.62 ( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 0.96/1.62 ( X ) ) }.
% 0.96/1.62 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.96/1.62 }.
% 0.96/1.62 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.96/1.62 ) ) }.
% 0.96/1.62 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.96/1.62 .
% 0.96/1.62 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.96/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.62 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 0.96/1.62 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 0.96/1.62 { v_s____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.96/1.62 tc_Complex_Ocomplex ) ) }.
% 0.96/1.62
% 0.96/1.62 *** allocated 15000 integers for clauses
% 0.96/1.62 *** allocated 22500 integers for clauses
% 0.96/1.62 *** allocated 33750 integers for clauses
% 0.96/1.62 *** allocated 50625 integers for clauses
% 0.96/1.62 *** allocated 75937 integers for clauses
% 0.96/1.62 percentage equality = 0.276962, percentage horn = 0.904129
% 0.96/1.62 This is a problem with some equality
% 0.96/1.62
% 0.96/1.62
% 0.96/1.62
% 0.96/1.62 Options Used:
% 0.96/1.62
% 0.96/1.62 useres = 1
% 0.96/1.62 useparamod = 1
% 0.96/1.62 useeqrefl = 1
% 0.96/1.62 useeqfact = 1
% 0.96/1.62 usefactor = 1
% 0.96/1.62 usesimpsplitting = 0
% 0.96/1.62 usesimpdemod = 5
% 0.96/1.62 usesimpres = 3
% 0.96/1.62
% 0.96/1.62 resimpinuse = 1000
% 0.96/1.62 resimpclauses = 20000
% 0.96/1.62 substype = eqrewr
% 0.96/1.62 backwardsubs = 1
% 0.96/1.62 selectoldest = 5
% 0.96/1.62
% 0.96/1.62 litorderings [0] = split
% 0.96/1.62 litorderings [1] = extend the termordering, first sorting on arguments
% 0.96/1.62
% 0.96/1.62 termordering = kbo
% 0.96/1.62
% 0.96/1.62 litapriori = 0
% 0.96/1.62 termapriori = 1
% 0.96/1.62 litaposteriori = 0
% 0.96/1.62 termaposteriori = 0
% 0.96/1.62 demodaposteriori = 0
% 0.96/1.62 ordereqreflfact = 0
% 0.96/1.62
% 0.96/1.62 litselect = negord
% 0.96/1.62
% 0.96/1.62 maxweight = 15
% 0.96/1.62 maxdepth = 30000
% 0.96/1.62 maxlength = 115
% 0.96/1.62 maxnrvars = 195
% 0.96/1.62 excuselevel = 1
% 0.96/1.62 increasemaxweight = 1
% 0.96/1.62
% 0.96/1.62 maxselected = 10000000
% 0.96/1.62 maxnrclauses = 10000000
% 0.96/1.62
% 0.96/1.62 showgenerated = 0
% 0.96/1.62 showkept = 0
% 0.96/1.62 showselected = 0
% 0.96/1.62 showdeleted = 0
% 0.96/1.62 showresimp = 1
% 0.96/1.62 showstatus = 2000
% 0.96/1.62
% 0.96/1.62 prologoutput = 0
% 0.96/1.62 nrgoals = 5000000
% 0.96/1.62 totalproof = 1
% 0.96/1.62
% 0.96/1.62 Symbols occurring in the translation:
% 0.96/1.62
% 0.96/1.62 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.96/1.62 . [1, 2] (w:1, o:195, a:1, s:1, b:0),
% 0.96/1.62 ! [4, 1] (w:0, o:113, a:1, s:1, b:0),
% 0.96/1.62 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.96/1.62 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.96/1.62 hAPP [38, 2] (w:1, o:219, a:1, s:1, b:0),
% 0.96/1.62 v_pa____ [39, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.96/1.62 tc_Complex_Ocomplex [40, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.96/1.62 tc_Polynomial_Opoly [41, 1] (w:1, o:119, a:1, s:1, b:0),
% 0.96/1.62 c_Groups_Ozero__class_Ozero [42, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.96/1.62 v_qa____ [43, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.96/1.62 class_Groups_Ozero [46, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Ocomm__semiring__0 [48, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.96/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [49, 3] (w:1
% 0.96/1.62 , o:247, a:1, s:1, b:0),
% 0.96/1.62 v_n [52, 0] (w:1, o:30, a:1, s:1, b:0),
% 0.96/1.62 tc_Nat_Onat [53, 0] (w:1, o:31, a:1, s:1, b:0),
% 0.96/1.62 c_Polynomial_Opoly__rec [56, 5] (w:1, o:293, a:1, s:1, b:0),
% 0.96/1.62 c_Polynomial_Omonom [58, 3] (w:1, o:251, a:1, s:1, b:0),
% 0.96/1.62 c_Polynomial_Opoly [62, 2] (w:1, o:220, a:1, s:1, b:0),
% 0.96/1.62 c_Polynomial_Ocoeff [63, 2] (w:1, o:221, a:1, s:1, b:0),
% 0.96/1.62 c_Polynomial_Osmult [65, 3] (w:1, o:252, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Oidom [66, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.96/1.62 v_p [67, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.96/1.62 v_q [68, 0] (w:1, o:53, a:1, s:1, b:0),
% 0.96/1.62 v_na____ [69, 0] (w:1, o:54, a:1, s:1, b:0),
% 0.96/1.62 v_a____ [70, 0] (w:1, o:55, a:1, s:1, b:0),
% 0.96/1.62 class_Int_Oring__char__0 [73, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.96/1.62 c_Polynomial_Odegree [78, 2] (w:1, o:222, a:1, s:1, b:0),
% 0.96/1.62 c_Polynomial_Oorder [79, 3] (w:1, o:253, a:1, s:1, b:0),
% 0.96/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [80, 2] (w:1, o:223
% 0.96/1.62 , a:1, s:1, b:0),
% 0.96/1.62 c_Polynomial_OpCons [81, 3] (w:1, o:254, a:1, s:1, b:0),
% 0.96/1.62 class_Fields_Ofield [82, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.96/1.62 c_Rings_Odvd__class_Odvd [83, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.96/1.62 hBOOL [84, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.96/1.62 c_Polynomial_Opcompose [86, 3] (w:1, o:255, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Ocomm__semiring__1 [87, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.96/1.62 c_fequal [89, 2] (w:1, o:224, a:1, s:1, b:0),
% 0.96/1.62 c_If [90, 4] (w:1, o:281, a:1, s:1, b:0),
% 0.96/1.62 c_Power_Opower__class_Opower [91, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq [92, 3] (w:1, o:249, a:1, s:1, b:0)
% 0.96/1.62 ,
% 0.96/1.62 c_Polynomial_Osynthetic__div [94, 3] (w:1, o:256, a:1, s:1, b:0),
% 0.96/1.62 c_Nat_OSuc [95, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.96/1.62 c_Groups_Otimes__class_Otimes [96, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.96/1.62 c_Groups_Ouminus__class_Ouminus [97, 2] (w:1, o:225, a:1, s:1, b:0),
% 0.96/1.62
% 0.96/1.62 c_Groups_Oone__class_Oone [98, 1] (w:1, o:137, a:1, s:1, b:0),
% 0.96/1.62 v_s____ [99, 0] (w:1, o:68, a:1, s:1, b:0),
% 0.96/1.62 c_Orderings_Oord__class_Oless [101, 3] (w:1, o:250, a:1, s:1, b:0),
% 0.96/1.62 c_Nat_Onat_Onat__case [104, 3] (w:1, o:248, a:1, s:1, b:0),
% 0.96/1.62 v_r____ [105, 0] (w:1, o:67, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Olinordered__semidom [106, 1] (w:1, o:140, a:1, s:1, b:0)
% 0.96/1.62 ,
% 0.96/1.62 class_Rings_Olinordered__ring [107, 1] (w:1, o:138, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Olinordered__ring__strict [108, 1] (w:1, o:139, a:1, s:1
% 0.96/1.62 , b:0),
% 0.96/1.62 class_Rings_Olinordered__idom [109, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Olinordered__semiring__strict [111, 1] (w:1, o:142, a:1
% 0.96/1.62 , s:1, b:0),
% 0.96/1.62 class_Rings_Oordered__cancel__semiring [112, 1] (w:1, o:147, a:1, s:1
% 0.96/1.62 , b:0),
% 0.96/1.62 class_Rings_Oordered__ring [114, 1] (w:1, o:148, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Olinordered__comm__semiring__strict [115, 1] (w:1, o:149
% 0.96/1.62 , a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Oordered__semiring [116, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.96/1.62
% 0.96/1.62 class_Rings_Oordered__comm__semiring [117, 1] (w:1, o:151, a:1, s:1
% 0.96/1.62 , b:0),
% 0.96/1.62 class_Rings_Olinordered__semiring [119, 1] (w:1, o:152, a:1, s:1, b:0
% 0.96/1.62 ),
% 0.96/1.62 class_Rings_Oring [120, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Oring__1__no__zero__divisors [121, 1] (w:1, o:154, a:1
% 0.96/1.62 , s:1, b:0),
% 0.96/1.62 class_Groups_Oordered__ab__group__add [122, 1] (w:1, o:155, a:1, s:1
% 0.96/1.62 , b:0),
% 0.96/1.62 class_Groups_Oab__semigroup__mult [123, 1] (w:1, o:156, a:1, s:1, b:0
% 0.96/1.62 ),
% 0.96/1.62 class_Groups_Ogroup__add [124, 1] (w:1, o:157, a:1, s:1, b:0),
% 0.96/1.62 class_Groups_Ocomm__monoid__mult [125, 1] (w:1, o:158, a:1, s:1, b:0)
% 0.96/1.62 ,
% 0.96/1.62 class_Groups_Omonoid__mult [126, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.96/1.62 class_Groups_Oone [127, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.96/1.62 class_Groups_Olinordered__ab__group__add [128, 1] (w:1, o:159, a:1
% 0.96/1.62 , s:1, b:0),
% 0.96/1.62 class_Rings_Ocomm__ring__1 [129, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.96/1.62 class_Groups_Oab__group__add [130, 1] (w:1, o:162, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Ocomm__ring [131, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Ono__zero__divisors [132, 1] (w:1, o:146, a:1, s:1, b:0)
% 0.96/1.62 ,
% 0.96/1.62 class_Rings_Oring__no__zero__divisors [133, 1] (w:1, o:163, a:1, s:1
% 0.96/1.62 , b:0),
% 0.96/1.62 class_Rings_Omult__zero [134, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Ozero__neq__one [135, 1] (w:1, o:164, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Odvd [137, 1] (w:1, o:166, a:1, s:1, b:0),
% 0.96/1.62 class_Power_Opower [155, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Osemiring__0 [156, 1] (w:1, o:173, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Oring__1 [158, 1] (w:1, o:172, a:1, s:1, b:0),
% 0.96/1.62 tc_Int_Oint [165, 0] (w:1, o:98, a:1, s:1, b:0),
% 0.96/1.62 class_Orderings_Opreorder [166, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.96/1.62 c_Power_Opower_Opower [167, 3] (w:1, o:257, a:1, s:1, b:0),
% 0.96/1.62 c_Groups_Oplus__class_Oplus [168, 3] (w:1, o:258, a:1, s:1, b:0),
% 0.96/1.62 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 3.53/3.92 169, 1] (w:1, o:178, a:1, s:1, b:0),
% 3.53/3.92 class_Groups_Ocomm__monoid__add [172, 1] (w:1, o:179, a:1, s:1, b:0)
% 3.53/3.92 ,
% 3.53/3.92 class_Groups_Omonoid__add [173, 1] (w:1, o:180, a:1, s:1, b:0),
% 3.53/3.92 class_Groups_Oordered__ab__semigroup__add__imp__le [174, 1] (w:1, o:
% 3.53/3.92 181, a:1, s:1, b:0),
% 3.53/3.92 class_Groups_Oordered__ab__semigroup__add [175, 1] (w:1, o:182, a:1
% 3.53/3.92 , s:1, b:0),
% 3.53/3.92 class_Groups_Oordered__cancel__ab__semigroup__add [176, 1] (w:1, o:
% 3.53/3.92 183, a:1, s:1, b:0),
% 3.53/3.92 class_Rings_Ocomm__semiring [177, 1] (w:1, o:165, a:1, s:1, b:0),
% 3.53/3.92 class_Rings_Osemiring [179, 1] (w:1, o:174, a:1, s:1, b:0),
% 3.53/3.92 class_Groups_Oab__semigroup__add [180, 1] (w:1, o:184, a:1, s:1, b:0)
% 3.53/3.92 ,
% 3.53/3.92 class_Groups_Ocancel__semigroup__add [181, 1] (w:1, o:185, a:1, s:1
% 3.53/3.92 , b:0),
% 3.53/3.92 class_Groups_Ocancel__ab__semigroup__add [182, 1] (w:1, o:186, a:1
% 3.53/3.92 , s:1, b:0),
% 3.53/3.92 class_Groups_Oordered__comm__monoid__add [183, 1] (w:1, o:187, a:1
% 3.53/3.92 , s:1, b:0),
% 3.53/3.92 class_Orderings_Olinorder [186, 1] (w:1, o:170, a:1, s:1, b:0),
% 3.53/3.92 class_Orderings_Oord [187, 1] (w:1, o:167, a:1, s:1, b:0),
% 3.53/3.92 tc_fun [188, 2] (w:1, o:236, a:1, s:1, b:0),
% 3.53/3.92 class_Orderings_Oorder [189, 1] (w:1, o:168, a:1, s:1, b:0),
% 3.53/3.92 class_Rings_Olinordered__semiring__1 [192, 1] (w:1, o:143, a:1, s:1
% 3.53/3.92 , b:0),
% 3.53/3.92 class_Rings_Olinordered__semiring__1__strict [193, 1] (w:1, o:144, a:
% 3.53/3.92 1, s:1, b:0),
% 3.53/3.92 c_Polynomial_Opdivmod__rel [196, 5] (w:1, o:294, a:1, s:1, b:0),
% 3.53/3.92 c_Polynomial_Opos__poly [205, 2] (w:1, o:237, a:1, s:1, b:0),
% 3.53/3.92 class_RealVector_Oreal__normed__algebra [206, 1] (w:1, o:175, a:1, s:
% 3.53/3.92 1, b:0),
% 3.53/3.92 class_Lattices_Oboolean__algebra [217, 1] (w:1, o:189, a:1, s:1, b:0)
% 3.53/3.92 ,
% 3.53/3.92 class_Lattices_Oab__semigroup__idem__mult [218, 1] (w:1, o:188, a:1
% 3.53/3.92 , s:1, b:0),
% 3.53/3.92 class_Groups_Ouminus [220, 1] (w:1, o:190, a:1, s:1, b:0),
% 3.53/3.92 c_Polynomial_Opoly__gcd [222, 3] (w:1, o:259, a:1, s:1, b:0),
% 3.53/3.92 c_Polynomial_OAbs__poly [223, 2] (w:1, o:238, a:1, s:1, b:0),
% 3.53/3.92 c_Rings_Oinverse__class_Oinverse [224, 2] (w:1, o:239, a:1, s:1, b:0)
% 3.53/3.92 ,
% 3.53/3.92 class_Rings_Odivision__ring__inverse__zero [225, 1] (w:1, o:176, a:1
% 3.53/3.92 , s:1, b:0),
% 3.53/3.92 class_Rings_Odivision__ring [226, 1] (w:1, o:177, a:1, s:1, b:0),
% 3.53/3.92 class_Fields_Olinordered__field [227, 1] (w:1, o:122, a:1, s:1, b:0)
% 3.53/3.92 ,
% 3.53/3.92 class_Fields_Olinordered__field__inverse__zero [228, 1] (w:1, o:123
% 3.53/3.92 , a:1, s:1, b:0),
% 3.53/3.92 class_Fields_Ofield__inverse__zero [229, 1] (w:1, o:124, a:1, s:1, b:
% 3.53/3.92 0),
% 3.53/3.92 c_Divides_Odiv__class_Omod [230, 3] (w:1, o:260, a:1, s:1, b:0),
% 3.53/3.92 class_Divides_Oring__div [232, 1] (w:1, o:191, a:1, s:1, b:0),
% 3.53/3.92 class_Divides_Osemiring__div [233, 1] (w:1, o:192, a:1, s:1, b:0),
% 3.53/3.92 c_Groups_Ominus__class_Ominus [234, 3] (w:1, o:261, a:1, s:1, b:0),
% 3.53/3.92 c_Orderings_Oorder_Omono [235, 4] (w:1, o:282, a:1, s:1, b:0),
% 3.53/3.92 class_Groups_Ominus [239, 1] (w:1, o:193, a:1, s:1, b:0),
% 3.53/3.92 class_Groups_Ocancel__comm__monoid__add [243, 1] (w:1, o:194, a:1, s:
% 3.53/3.92 1, b:0),
% 3.53/3.92 tc_HOL_Obool [245, 0] (w:1, o:97, a:1, s:1, b:0),
% 3.53/3.92 alpha1 [246, 3] (w:1, o:262, a:1, s:1, b:1),
% 3.53/3.92 alpha2 [247, 3] (w:1, o:267, a:1, s:1, b:1),
% 3.53/3.92 alpha3 [248, 3] (w:1, o:272, a:1, s:1, b:1),
% 3.53/3.92 alpha4 [249, 4] (w:1, o:283, a:1, s:1, b:1),
% 3.53/3.92 alpha5 [250, 4] (w:1, o:284, a:1, s:1, b:1),
% 3.53/3.92 alpha6 [251, 2] (w:1, o:240, a:1, s:1, b:1),
% 3.53/3.92 alpha7 [252, 2] (w:1, o:241, a:1, s:1, b:1),
% 3.53/3.92 alpha8 [253, 2] (w:1, o:242, a:1, s:1, b:1),
% 3.53/3.92 alpha9 [254, 3] (w:1, o:273, a:1, s:1, b:1),
% 3.53/3.92 alpha10 [255, 2] (w:1, o:243, a:1, s:1, b:1),
% 3.53/3.92 alpha11 [256, 2] (w:1, o:244, a:1, s:1, b:1),
% 3.53/3.92 alpha12 [257, 3] (w:1, o:263, a:1, s:1, b:1),
% 3.53/3.92 alpha13 [258, 4] (w:1, o:285, a:1, s:1, b:1),
% 3.53/3.92 alpha14 [259, 3] (w:1, o:264, a:1, s:1, b:1),
% 3.53/3.92 alpha15 [260, 3] (w:1, o:265, a:1, s:1, b:1),
% 3.53/3.92 alpha16 [261, 4] (w:1, o:286, a:1, s:1, b:1),
% 3.53/3.92 alpha17 [262, 4] (w:1, o:287, a:1, s:1, b:1),
% 3.53/3.92 alpha18 [263, 3] (w:1, o:266, a:1, s:1, b:1),
% 3.53/3.92 alpha19 [264, 2] (w:1, o:245, a:1, s:1, b:1),
% 3.53/3.92 alpha20 [265, 2] (w:1, o:246, a:1, s:1, b:1),
% 19.99/20.35 alpha21 [266, 4] (w:1, o:288, a:1, s:1, b:1),
% 19.99/20.35 alpha22 [267, 3] (w:1, o:268, a:1, s:1, b:1),
% 19.99/20.35 alpha23 [268, 3] (w:1, o:269, a:1, s:1, b:1),
% 19.99/20.35 alpha24 [269, 3] (w:1, o:270, a:1, s:1, b:1),
% 19.99/20.35 alpha25 [270, 3] (w:1, o:271, a:1, s:1, b:1),
% 19.99/20.35 alpha26 [271, 4] (w:1, o:289, a:1, s:1, b:1),
% 19.99/20.35 alpha27 [272, 4] (w:1, o:290, a:1, s:1, b:1),
% 19.99/20.35 alpha28 [273, 4] (w:1, o:291, a:1, s:1, b:1),
% 19.99/20.35 skol1 [274, 2] (w:1, o:226, a:1, s:1, b:1),
% 19.99/20.35 skol2 [275, 3] (w:1, o:277, a:1, s:1, b:1),
% 19.99/20.35 skol3 [276, 2] (w:1, o:228, a:1, s:1, b:1),
% 19.99/20.35 skol4 [277, 0] (w:1, o:15, a:1, s:1, b:1),
% 19.99/20.35 skol5 [278, 0] (w:1, o:16, a:1, s:1, b:1),
% 19.99/20.35 skol6 [279, 2] (w:1, o:229, a:1, s:1, b:1),
% 19.99/20.35 skol7 [280, 1] (w:1, o:118, a:1, s:1, b:1),
% 19.99/20.35 skol8 [281, 3] (w:1, o:278, a:1, s:1, b:1),
% 19.99/20.35 skol9 [282, 3] (w:1, o:279, a:1, s:1, b:1),
% 19.99/20.35 skol10 [283, 2] (w:1, o:230, a:1, s:1, b:1),
% 19.99/20.35 skol11 [284, 2] (w:1, o:231, a:1, s:1, b:1),
% 19.99/20.35 skol12 [285, 2] (w:1, o:232, a:1, s:1, b:1),
% 19.99/20.35 skol13 [286, 3] (w:1, o:274, a:1, s:1, b:1),
% 19.99/20.35 skol14 [287, 2] (w:1, o:233, a:1, s:1, b:1),
% 19.99/20.35 skol15 [288, 2] (w:1, o:234, a:1, s:1, b:1),
% 19.99/20.35 skol16 [289, 4] (w:1, o:292, a:1, s:1, b:1),
% 19.99/20.35 skol17 [290, 3] (w:1, o:275, a:1, s:1, b:1),
% 19.99/20.35 skol18 [291, 3] (w:1, o:276, a:1, s:1, b:1),
% 19.99/20.35 skol19 [292, 2] (w:1, o:235, a:1, s:1, b:1),
% 19.99/20.35 skol20 [293, 2] (w:1, o:227, a:1, s:1, b:1),
% 19.99/20.35 skol21 [294, 3] (w:1, o:280, a:1, s:1, b:1).
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Starting Search:
% 19.99/20.35
% 19.99/20.35 *** allocated 113905 integers for clauses
% 19.99/20.35 *** allocated 170857 integers for clauses
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 3102
% 19.99/20.35 Kept: 2035
% 19.99/20.35 Inuse: 54
% 19.99/20.35 Deleted: 2
% 19.99/20.35 Deletedinuse: 0
% 19.99/20.35
% 19.99/20.35 *** allocated 256285 integers for clauses
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 *** allocated 170857 integers for termspace/termends
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 *** allocated 384427 integers for clauses
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 9823
% 19.99/20.35 Kept: 4438
% 19.99/20.35 Inuse: 149
% 19.99/20.35 Deleted: 3
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 *** allocated 256285 integers for termspace/termends
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 14771
% 19.99/20.35 Kept: 6479
% 19.99/20.35 Inuse: 204
% 19.99/20.35 Deleted: 3
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 *** allocated 576640 integers for clauses
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 19166
% 19.99/20.35 Kept: 8621
% 19.99/20.35 Inuse: 244
% 19.99/20.35 Deleted: 3
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 *** allocated 384427 integers for termspace/termends
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 23387
% 19.99/20.35 Kept: 10628
% 19.99/20.35 Inuse: 277
% 19.99/20.35 Deleted: 5
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 *** allocated 864960 integers for clauses
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 31284
% 19.99/20.35 Kept: 12642
% 19.99/20.35 Inuse: 297
% 19.99/20.35 Deleted: 5
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 *** allocated 576640 integers for termspace/termends
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 36272
% 19.99/20.35 Kept: 14930
% 19.99/20.35 Inuse: 327
% 19.99/20.35 Deleted: 5
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 42634
% 19.99/20.35 Kept: 17280
% 19.99/20.35 Inuse: 352
% 19.99/20.35 Deleted: 5
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 *** allocated 1297440 integers for clauses
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 48662
% 19.99/20.35 Kept: 19744
% 19.99/20.35 Inuse: 367
% 19.99/20.35 Deleted: 5
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 Resimplifying clauses:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 *** allocated 864960 integers for termspace/termends
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 54703
% 19.99/20.35 Kept: 22427
% 19.99/20.35 Inuse: 397
% 19.99/20.35 Deleted: 122
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 61841
% 19.99/20.35 Kept: 24858
% 19.99/20.35 Inuse: 417
% 19.99/20.35 Deleted: 122
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 70715
% 19.99/20.35 Kept: 26907
% 19.99/20.35 Inuse: 437
% 19.99/20.35 Deleted: 122
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 *** allocated 1946160 integers for clauses
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 75354
% 19.99/20.35 Kept: 29003
% 19.99/20.35 Inuse: 477
% 19.99/20.35 Deleted: 122
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 *** allocated 1297440 integers for termspace/termends
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 80100
% 19.99/20.35 Kept: 31035
% 19.99/20.35 Inuse: 522
% 19.99/20.35 Deleted: 122
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 84841
% 19.99/20.35 Kept: 33053
% 19.99/20.35 Inuse: 562
% 19.99/20.35 Deleted: 122
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 94111
% 19.99/20.35 Kept: 35082
% 19.99/20.35 Inuse: 622
% 19.99/20.35 Deleted: 122
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 103788
% 19.99/20.35 Kept: 37239
% 19.99/20.35 Inuse: 677
% 19.99/20.35 Deleted: 122
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 113420
% 19.99/20.35 Kept: 39302
% 19.99/20.35 Inuse: 712
% 19.99/20.35 Deleted: 122
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 Resimplifying clauses:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 118704
% 19.99/20.35 Kept: 41319
% 19.99/20.35 Inuse: 752
% 19.99/20.35 Deleted: 155
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 *** allocated 2919240 integers for clauses
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 126030
% 19.99/20.35 Kept: 43320
% 19.99/20.35 Inuse: 786
% 19.99/20.35 Deleted: 155
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 *** allocated 1946160 integers for termspace/termends
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 133308
% 19.99/20.35 Kept: 45510
% 19.99/20.35 Inuse: 812
% 19.99/20.35 Deleted: 155
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 144787
% 19.99/20.35 Kept: 47525
% 19.99/20.35 Inuse: 837
% 19.99/20.35 Deleted: 155
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 150821
% 19.99/20.35 Kept: 49530
% 19.99/20.35 Inuse: 871
% 19.99/20.35 Deleted: 155
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 160863
% 19.99/20.35 Kept: 51684
% 19.99/20.35 Inuse: 882
% 19.99/20.35 Deleted: 155
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 180278
% 19.99/20.35 Kept: 55056
% 19.99/20.35 Inuse: 897
% 19.99/20.35 Deleted: 155
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 191237
% 19.99/20.35 Kept: 57463
% 19.99/20.35 Inuse: 912
% 19.99/20.35 Deleted: 155
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 205852
% 19.99/20.35 Kept: 61101
% 19.99/20.35 Inuse: 947
% 19.99/20.35 Deleted: 155
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 Resimplifying clauses:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 *** allocated 2919240 integers for termspace/termends
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 217028
% 19.99/20.35 Kept: 64220
% 19.99/20.35 Inuse: 967
% 19.99/20.35 Deleted: 333
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 *** allocated 4378860 integers for clauses
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 227479
% 19.99/20.35 Kept: 67776
% 19.99/20.35 Inuse: 992
% 19.99/20.35 Deleted: 333
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 239028
% 19.99/20.35 Kept: 69874
% 19.99/20.35 Inuse: 1032
% 19.99/20.35 Deleted: 333
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 250429
% 19.99/20.35 Kept: 71890
% 19.99/20.35 Inuse: 1071
% 19.99/20.35 Deleted: 333
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 256340
% 19.99/20.35 Kept: 73894
% 19.99/20.35 Inuse: 1101
% 19.99/20.35 Deleted: 333
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 273844
% 19.99/20.35 Kept: 77031
% 19.99/20.35 Inuse: 1112
% 19.99/20.35 Deleted: 333
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Intermediate Status:
% 19.99/20.35 Generated: 289787
% 19.99/20.35 Kept: 79490
% 19.99/20.35 Inuse: 1117
% 19.99/20.35 Deleted: 333
% 19.99/20.35 Deletedinuse: 1
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 Resimplifying inuse:
% 19.99/20.35 Done
% 19.99/20.35
% 19.99/20.35 Resimplifying clauses:
% 19.99/20.35
% 19.99/20.35 Bliksems!, er is een bewijs:
% 19.99/20.35 % SZS status Theorem
% 19.99/20.35 % SZS output start Refutation
% 19.99/20.35
% 19.99/20.35 (1) {G0,W5,D4,L1,V0,M1} I { ! c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) ==> v_pa____ }.
% 19.99/20.35 (84) {G0,W29,D10,L1,V0,M1} I { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.35 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.35 ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 19.99/20.35 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 19.99/20.35 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 19.99/20.35 tc_Complex_Ocomplex ) ) ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex,
% 19.99/20.35 v_a____, v_pa____ ) ) ), v_s____ ) ==> v_pa____ }.
% 19.99/20.35 (232) {G0,W15,D5,L3,V3,M3} I { ! class_Rings_Oring__no__zero__divisors( X )
% 19.99/20.35 , ! Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ==>
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (1321) {G0,W2,D2,L1,V0,M1} I { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 19.99/20.35 (1337) {G0,W5,D3,L2,V1,M2} I { ! class_Rings_Oidom( X ),
% 19.99/20.35 class_Rings_Oring__no__zero__divisors( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (1384) {G0,W5,D4,L1,V0,M1} I { c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) ==> v_s____ }.
% 19.99/20.35 (1691) {G1,W3,D2,L1,V0,M1} S(1);d(1384) { ! v_s____ ==> v_pa____ }.
% 19.99/20.35 (20175) {G1,W27,D9,L1,V0,M1} S(84);d(1384) { hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.35 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 19.99/20.35 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 19.99/20.35 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 19.99/20.35 tc_Complex_Ocomplex ), v_s____ ) ) ), c_Polynomial_Oorder(
% 19.99/20.35 tc_Complex_Ocomplex, v_a____, v_pa____ ) ) ), v_s____ ) ==> v_pa____ }.
% 19.99/20.35 (29050) {G1,W3,D3,L1,V0,M1} R(1337,1321) {
% 19.99/20.35 class_Rings_Oring__no__zero__divisors( tc_Polynomial_Opoly(
% 19.99/20.35 tc_Complex_Ocomplex ) ) }.
% 19.99/20.35 (80322) {G2,W12,D6,L2,V2,M2} R(232,29050);d(1384);d(1384) { ! X = v_s____,
% 19.99/20.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly(
% 19.99/20.35 tc_Complex_Ocomplex ) ), Y ), X ) ==> v_s____ }.
% 19.99/20.35 (80594) {G3,W9,D6,L1,V1,M1} Q(80322) { hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.35 ), X ), v_s____ ) ==> v_s____ }.
% 19.99/20.35 (81244) {G4,W0,D0,L0,V0,M0} S(20175);d(80594);r(1691) { }.
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 % SZS output end Refutation
% 19.99/20.35 found a proof!
% 19.99/20.35
% 19.99/20.35
% 19.99/20.35 Unprocessed initial clauses:
% 19.99/20.35
% 19.99/20.35 (81246) {G0,W14,D4,L2,V2,M2} { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1
% 19.99/20.35 ( X, Y ) ), Y = X }.
% 19.99/20.35 (81247) {G0,W5,D4,L1,V0,M1} { ! v_pa____ = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) }.
% 19.99/20.35 (81248) {G0,W5,D4,L1,V0,M1} { ! v_qa____ = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) }.
% 19.99/20.35 (81249) {G0,W10,D3,L3,V2,M3} { ! class_Groups_Ozero( X ), !
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) = Y, Y = c_Groups_Ozero__class_Ozero( X
% 19.99/20.35 ) }.
% 19.99/20.35 (81250) {G0,W10,D3,L3,V2,M3} { ! class_Groups_Ozero( X ), ! Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) = Y
% 19.99/20.35 }.
% 19.99/20.35 (81251) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.35 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81252) {G0,W15,D4,L3,V3,M3} { ! class_Rings_Ocomm__semiring__0( X ), !
% 19.99/20.35 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81253) {G0,W15,D4,L3,V3,M3} { ! class_Rings_Ocomm__semiring__0( X ), ! Z
% 19.99/20.35 = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81254) {G0,W4,D3,L1,V0,M1} { ! v_n = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ) }.
% 19.99/20.35 (81255) {G0,W24,D6,L3,V4,M3} { ! class_Groups_Ozero( X ), ! hAPP( hAPP(
% 19.99/20.35 hAPP( Z, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero
% 19.99/20.35 ( tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y
% 19.99/20.35 , Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 19.99/20.35 (81256) {G0,W11,D4,L2,V2,M2} { ! class_Groups_Ozero( X ),
% 19.99/20.35 c_Polynomial_Omonom( X, c_Groups_Ozero__class_Ozero( X ), Y ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81257) {G0,W14,D4,L3,V3,M3} { ! class_Groups_Ozero( X ), !
% 19.99/20.35 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81258) {G0,W14,D4,L3,V3,M3} { ! class_Groups_Ozero( X ), ! Z =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), c_Polynomial_Omonom( X, Z, Y ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81259) {G0,W12,D6,L2,V2,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 19.99/20.35 ( c_Polynomial_Opoly( X, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 19.99/20.35 ( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81260) {G0,W12,D6,L2,V2,M2} { ! class_Groups_Ozero( X ), hAPP(
% 19.99/20.35 c_Polynomial_Ocoeff( X, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 19.99/20.35 ( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81261) {G0,W11,D4,L2,V2,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.35 c_Polynomial_Osmult( X, c_Groups_Ozero__class_Ozero( X ), Y ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81262) {G0,W19,D4,L4,V3,M4} { ! class_Rings_Oidom( X ), !
% 19.99/20.35 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81263) {G0,W14,D4,L3,V3,M3} { ! class_Rings_Oidom( X ), ! Z =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), c_Polynomial_Osmult( X, Z, Y ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81264) {G0,W15,D4,L3,V3,M3} { ! class_Rings_Oidom( X ), ! Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81265) {G0,W16,D4,L2,V1,M2} { ! hAPP( c_Polynomial_Opoly(
% 19.99/20.35 tc_Complex_Ocomplex, v_p ), X ) = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Complex_Ocomplex ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q
% 19.99/20.35 ), X ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 19.99/20.35 (81266) {G0,W4,D3,L1,V0,M1} { ! v_na____ = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ) }.
% 19.99/20.35 (81267) {G0,W16,D4,L2,V1,M2} { ! hAPP( c_Polynomial_Opoly(
% 19.99/20.35 tc_Complex_Ocomplex, v_pa____ ), X ) = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Complex_Ocomplex ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 19.99/20.35 v_qa____ ), X ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 19.99/20.35 (81268) {G0,W8,D4,L1,V0,M1} { hAPP( c_Polynomial_Opoly(
% 19.99/20.35 tc_Complex_Ocomplex, v_pa____ ), v_a____ ) = c_Groups_Ozero__class_Ozero
% 19.99/20.35 ( tc_Complex_Ocomplex ) }.
% 19.99/20.35 (81269) {G0,W16,D4,L3,V4,M3} { ! class_Groups_Ozero( X ), ! Z = Y, hAPP(
% 19.99/20.35 c_Polynomial_Ocoeff( X, Z ), T ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T )
% 19.99/20.35 }.
% 19.99/20.35 (81270) {G0,W22,D4,L3,V3,M3} { ! class_Groups_Ozero( X ), ! hAPP(
% 19.99/20.35 c_Polynomial_Ocoeff( X, Z ), skol2( X, Y, Z ) ) = hAPP(
% 19.99/20.35 c_Polynomial_Ocoeff( X, Y ), skol2( X, Y, Z ) ), Z = Y }.
% 19.99/20.35 (81271) {G0,W14,D3,L4,V3,M4} { ! class_Int_Oring__char__0( X ), !
% 19.99/20.35 class_Rings_Oidom( X ), ! c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly
% 19.99/20.35 ( X, Y ), Z = Y }.
% 19.99/20.35 (81272) {G0,W14,D3,L4,V3,M4} { ! class_Int_Oring__char__0( X ), !
% 19.99/20.35 class_Rings_Oidom( X ), ! Z = Y, c_Polynomial_Opoly( X, Z ) =
% 19.99/20.35 c_Polynomial_Opoly( X, Y ) }.
% 19.99/20.35 (81273) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Ozero( X ), !
% 19.99/20.35 c_Polynomial_Ocoeff( X, Z ) = c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 19.99/20.35 (81274) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Ozero( X ), ! Z = Y,
% 19.99/20.35 c_Polynomial_Ocoeff( X, Z ) = c_Polynomial_Ocoeff( X, Y ) }.
% 19.99/20.35 (81275) {G0,W15,D5,L3,V4,M3} { ! class_Groups_Ozero( X ), ! T = Z, hAPP(
% 19.99/20.35 c_Polynomial_Ocoeff( X, c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 19.99/20.35 (81276) {G0,W16,D5,L3,V4,M3} { ! class_Groups_Ozero( X ), T = Z, hAPP(
% 19.99/20.35 c_Polynomial_Ocoeff( X, c_Polynomial_Omonom( X, Y, T ) ), Z ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81277) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ozero( X ), !
% 19.99/20.35 c_Polynomial_Omonom( X, T, Z ) = c_Polynomial_Omonom( X, Y, Z ), T = Y
% 19.99/20.35 }.
% 19.99/20.35 (81278) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ozero( X ), ! T = Y,
% 19.99/20.35 c_Polynomial_Omonom( X, T, Z ) = c_Polynomial_Omonom( X, Y, Z ) }.
% 19.99/20.35 (81279) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.35 c_Polynomial_Osmult( X, Y, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81280) {G0,W18,D5,L4,V2,M4} { ! class_Int_Oring__char__0( X ), !
% 19.99/20.35 class_Rings_Oidom( X ), ! c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly
% 19.99/20.35 ( X, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81281) {G0,W18,D5,L4,V2,M4} { ! class_Int_Oring__char__0( X ), !
% 19.99/20.35 class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly( X, Y ) =
% 19.99/20.35 c_Polynomial_Opoly( X, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 19.99/20.35 X ) ) ) }.
% 19.99/20.35 (81282) {G0,W5,D3,L1,V0,M1} { c_Polynomial_Odegree( tc_Complex_Ocomplex,
% 19.99/20.35 v_p ) = v_n }.
% 19.99/20.35 (81283) {G0,W22,D4,L4,V3,M4} { ! class_Rings_Oidom( X ), ! hAPP(
% 19.99/20.35 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 19.99/20.35 c_Polynomial_Oorder( X, Y, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 19.99/20.35 ) }.
% 19.99/20.35 (81284) {G0,W15,D4,L3,V3,M3} { ! class_Rings_Oidom( X ), ! Z =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP(
% 19.99/20.35 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81285) {G0,W17,D4,L3,V3,M3} { ! class_Rings_Oidom( X ),
% 19.99/20.35 c_Polynomial_Oorder( X, Y, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 19.99/20.35 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 X ) }.
% 19.99/20.35 (81286) {G0,W7,D3,L1,V0,M1} { ! c_Polynomial_Oorder( tc_Complex_Ocomplex,
% 19.99/20.35 v_a____, v_pa____ ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.35 (81287) {G0,W13,D4,L3,V2,M3} { ! class_Groups_Ozero( X ), !
% 19.99/20.35 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81288) {G0,W13,D4,L3,V2,M3} { ! class_Groups_Ozero( X ), ! Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.35 (81289) {G0,W5,D3,L1,V0,M1} { c_Polynomial_Odegree( tc_Complex_Ocomplex,
% 19.99/20.35 v_pa____ ) = v_na____ }.
% 19.99/20.35 (81290) {G0,W36,D6,L3,V6,M3} { ! class_Groups_Ozero( X ), ! hAPP( hAPP(
% 19.99/20.35 hAPP( Z, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero
% 19.99/20.35 ( tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y
% 19.99/20.35 , Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 19.99/20.35 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 19.99/20.35 (81291) {G0,W14,D5,L2,V2,M2} { ! class_Groups_Ozero( X ),
% 19.99/20.35 c_Polynomial_Omonom( X, Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 19.99/20.35 c_Polynomial_OpCons( X, Y, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ) ) }.
% 19.99/20.35 (81292) {G0,W17,D6,L3,V4,M3} { ! class_Fields_Ofield( X ), ! hBOOL( hAPP(
% 19.99/20.35 hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 c_Polynomial_Osmult( X, T, Z ) ), Y ) ), alpha1( X, Y, T ) }.
% 19.99/20.35 (81293) {G0,W18,D6,L3,V4,M3} { ! class_Fields_Ofield( X ), ! hBOOL( hAPP(
% 19.99/20.35 hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 c_Polynomial_Osmult( X, T, Z ) ), Y ) ), alpha13( X, Y, Z, T ) }.
% 19.99/20.35 (81294) {G0,W22,D6,L4,V4,M4} { ! class_Fields_Ofield( X ), ! alpha1( X, Y
% 19.99/20.35 , T ), ! alpha13( X, Y, Z, T ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult
% 19.99/20.35 ( X, T, Z ) ), Y ) ) }.
% 19.99/20.35 (81295) {G0,W17,D6,L3,V4,M3} { ! alpha13( X, Y, Z, T ), T =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) }.
% 19.99/20.35 (81296) {G0,W9,D3,L2,V4,M2} { ! T = c_Groups_Ozero__class_Ozero( X ),
% 19.99/20.35 alpha13( X, Y, Z, T ) }.
% 19.99/20.35 (81297) {G0,W13,D6,L2,V4,M2} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), alpha13
% 19.99/20.35 ( X, Y, Z, T ) }.
% 19.99/20.35 (81298) {G0,W13,D4,L3,V3,M3} { ! alpha1( X, Y, Z ), ! Z =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81299) {G0,W8,D3,L2,V3,M2} { Z = c_Groups_Ozero__class_Ozero( X ), alpha1
% 19.99/20.35 ( X, Y, Z ) }.
% 19.99/20.35 (81300) {G0,W9,D4,L2,V3,M2} { ! Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ), alpha1( X, Y, Z ) }.
% 19.99/20.35 (81301) {G0,W20,D5,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 19.99/20.35 ( c_Polynomial_Opoly( X, c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP
% 19.99/20.35 ( c_Polynomial_Opoly( X, T ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 19.99/20.35 (81302) {G0,W17,D4,L3,V2,M3} { ! class_Groups_Ozero( X ), Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! hAPP(
% 19.99/20.35 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81303) {G0,W17,D4,L3,V2,M3} { ! class_Groups_Ozero( X ), ! hAPP(
% 19.99/20.35 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81304) {G0,W17,D4,L3,V2,M3} { ! class_Groups_Ozero( X ), ! Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP(
% 19.99/20.35 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81305) {G0,W15,D4,L3,V3,M3} { ! class_Rings_Oidom( X ), ! Z =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), c_Polynomial_Odegree( X,
% 19.99/20.35 c_Polynomial_Osmult( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ) }.
% 19.99/20.35 (81306) {G0,W16,D4,L3,V3,M3} { ! class_Rings_Oidom( X ), Z =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), c_Polynomial_Odegree( X,
% 19.99/20.35 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 19.99/20.35 (81307) {G0,W14,D3,L3,V5,M3} { ! class_Groups_Ozero( X ), !
% 19.99/20.35 c_Polynomial_OpCons( X, U, T ) = c_Polynomial_OpCons( X, Z, Y ), U = Z
% 19.99/20.35 }.
% 19.99/20.35 (81308) {G0,W14,D3,L3,V5,M3} { ! class_Groups_Ozero( X ), !
% 19.99/20.35 c_Polynomial_OpCons( X, U, T ) = c_Polynomial_OpCons( X, Z, Y ), T = Y
% 19.99/20.35 }.
% 19.99/20.35 (81309) {G0,W17,D3,L4,V5,M4} { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y
% 19.99/20.35 , c_Polynomial_OpCons( X, U, T ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 19.99/20.35 (81310) {G0,W36,D6,L5,V3,M5} { ! class_Rings_Oidom( X ), ! hAPP(
% 19.99/20.35 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) = hAPP(
% 19.99/20.35 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ), ! hBOOL(
% 19.99/20.35 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y
% 19.99/20.35 ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 19.99/20.35 ( X ) ), Y ), Z ) ), Z = Y }.
% 19.99/20.35 (81311) {G0,W13,D6,L2,V2,M2} { ! class_Groups_Ozero( X ),
% 19.99/20.35 c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Y,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.35 (81312) {G0,W21,D6,L3,V4,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 19.99/20.35 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 c_Polynomial_Osmult( X, T, Z ) ), Y ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) }.
% 19.99/20.35 (81313) {G0,W21,D6,L3,V4,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 19.99/20.35 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ), Z ), c_Polynomial_Osmult( X, T, Y ) ) ) }.
% 19.99/20.35 (81314) {G0,W12,D4,L2,V3,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.35 c_Polynomial_Odegree( X,
% 19.99/20.35 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) =
% 19.99/20.35 c_Polynomial_Odegree( X, Z ) }.
% 19.99/20.35 (81315) {G0,W13,D5,L2,V1,M2} { ! class_Groups_Ozero( X ),
% 19.99/20.35 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81316) {G0,W14,D4,L3,V3,M3} { ! class_Groups_Ozero( X ), !
% 19.99/20.35 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81317) {G0,W15,D4,L3,V3,M3} { ! class_Groups_Ozero( X ), !
% 19.99/20.35 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81318) {G0,W19,D4,L4,V3,M4} { ! class_Groups_Ozero( X ), ! Z =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X, Z, Y ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81319) {G0,W10,D5,L2,V1,M2} { ! class_Groups_Ozero( X ),
% 19.99/20.35 c_Polynomial_Odegree( X, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 19.99/20.35 ( X ) ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.35 (81320) {G0,W13,D5,L2,V3,M2} { ! class_Groups_Ozero( X ), hAPP(
% 19.99/20.35 c_Polynomial_Ocoeff( X, c_Polynomial_OpCons( X, Z, Y ) ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 19.99/20.35 (81321) {G0,W25,D6,L4,V4,M4} { ! class_Fields_Ofield( X ), ! hBOOL( hAPP(
% 19.99/20.35 hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 19.99/20.35 c_Polynomial_Osmult( X, Z, Y ) ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 19.99/20.35 , T ), Y ) ) }.
% 19.99/20.35 (81322) {G0,W25,D6,L4,V4,M4} { ! class_Fields_Ofield( X ), ! hBOOL( hAPP(
% 19.99/20.35 hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), T
% 19.99/20.35 = c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult
% 19.99/20.35 ( X, T, Z ) ), Y ) ) }.
% 19.99/20.35 (81323) {G0,W25,D6,L4,V4,M4} { ! class_Fields_Ofield( X ), Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 19.99/20.35 c_Polynomial_Osmult( X, Y, Z ) ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Z ) ) }.
% 19.99/20.35 (81324) {G0,W25,D6,L4,V4,M4} { ! class_Fields_Ofield( X ), Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Z ) ), hBOOL(
% 19.99/20.35 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 19.99/20.35 c_Polynomial_Osmult( X, Y, Z ) ) ) }.
% 19.99/20.35 (81325) {G0,W14,D4,L3,V3,M3} { ! class_Groups_Ozero( X ), Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), c_Polynomial_Odegree( X,
% 19.99/20.35 c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 19.99/20.35 (81326) {G0,W16,D4,L3,V4,M3} { ! class_Rings_Ocomm__semiring__0( X ), !
% 19.99/20.35 c_Polynomial_Osmult( X, T, Y ) = c_Polynomial_OpCons( X, Z, Y ), Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81327) {G0,W32,D7,L2,V6,M2} { ! class_Groups_Ozero( X ),
% 19.99/20.35 c_Polynomial_Opoly__rec( W, X, U, T, c_Polynomial_OpCons( X, Z, Y ) ) =
% 19.99/20.35 hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W, c_fequal( Y,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), U,
% 19.99/20.35 c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 19.99/20.35 (81328) {G0,W18,D6,L2,V3,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.35 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 19.99/20.35 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 19.99/20.35 (81329) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.35 c_Polynomial_Opcompose( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81330) {G0,W19,D7,L2,V0,M2} { ! v_qa____ = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ),
% 19.99/20.35 v_pa____ ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly
% 19.99/20.35 ( tc_Complex_Ocomplex ) ), v_qa____ ), v_na____ ) ) ) }.
% 19.99/20.35 (81331) {G0,W10,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.35 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 19.99/20.35 (81332) {G0,W7,D3,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, c_Polynomial_Oorder( tc_Complex_Ocomplex, X, v_pa____ ),
% 19.99/20.35 v_na____ ) }.
% 19.99/20.35 (81333) {G0,W14,D5,L3,V2,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 19.99/20.35 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81334) {G0,W16,D4,L3,V3,M3} { ! class_Rings_Ocomm__semiring__0( X ), !
% 19.99/20.35 c_Polynomial_Osynthetic__div( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, Z ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.35 (81335) {G0,W16,D4,L3,V3,M3} { ! class_Rings_Ocomm__semiring__0( X ), !
% 19.99/20.35 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 19.99/20.35 , c_Polynomial_Osynthetic__div( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81336) {G0,W13,D4,L3,V2,M3} { ! class_Groups_Ozero( X ), ! Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.35 (81337) {G0,W15,D4,L3,V2,M3} { ! class_Groups_Ozero( X ), Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 19.99/20.35 c_Polynomial_Odegree( X, Y ) ) }.
% 19.99/20.35 (81338) {G0,W29,D10,L1,V0,M1} { v_pa____ = hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.35 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 19.99/20.35 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 19.99/20.35 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 19.99/20.35 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 19.99/20.35 tc_Complex_Ocomplex ) ) ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex,
% 19.99/20.35 v_a____, v_pa____ ) ) ), v_s____ ) }.
% 19.99/20.35 (81339) {G0,W37,D7,L5,V4,M5} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, X, v_na____ ), ! hAPP( c_Polynomial_Opoly(
% 19.99/20.35 tc_Complex_Ocomplex, Z ), skol3( T, Z ) ) = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Complex_Ocomplex ), ! c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) =
% 19.99/20.35 X, X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), Y
% 19.99/20.35 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 19.99/20.35 tc_Complex_Ocomplex ) ), Z ), X ) ) ) }.
% 19.99/20.35 (81340) {G0,W37,D7,L5,V3,M5} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, X, v_na____ ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex
% 19.99/20.35 , Y ), skol3( Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex
% 19.99/20.35 ), ! c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = X, X =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), Y
% 19.99/20.35 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 19.99/20.35 tc_Complex_Ocomplex ) ), Z ), X ) ) ) }.
% 19.99/20.35 (81341) {G0,W16,D4,L3,V3,M3} { ! class_Groups_Ozero( X ), ! Z =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Y, Z ) ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.35 (81342) {G0,W18,D4,L3,V3,M3} { ! class_Groups_Ozero( X ), Z =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Y, Z ) ) = c_Nat_OSuc(
% 19.99/20.35 c_Polynomial_Odegree( X, Z ) ) }.
% 19.99/20.35 (81343) {G0,W21,D5,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.35 c_Polynomial_Osynthetic__div( X, c_Polynomial_OpCons( X, T, Z ), Y ) =
% 19.99/20.35 c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Z ), Y ),
% 19.99/20.35 c_Polynomial_Osynthetic__div( X, Z, Y ) ) }.
% 19.99/20.35 (81344) {G0,W15,D4,L2,V3,M2} { ! class_Groups_Ozero( X ),
% 19.99/20.35 c_Polynomial_Ocoeff( X, c_Polynomial_OpCons( X, Z, Y ) ) =
% 19.99/20.35 c_Nat_Onat_Onat__case( X, Z, c_Polynomial_Ocoeff( X, Y ) ) }.
% 19.99/20.35 (81345) {G0,W20,D8,L1,V0,M1} { v_qa____ = hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.35 ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 19.99/20.35 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 19.99/20.35 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 19.99/20.35 tc_Complex_Ocomplex ) ) ) ) ), v_r____ ) }.
% 19.99/20.35 (81346) {G0,W19,D8,L1,V0,M1} { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 19.99/20.35 ( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 19.99/20.35 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 19.99/20.35 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 19.99/20.35 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 19.99/20.35 ) ) ), v_qa____ ) ) }.
% 19.99/20.35 (81347) {G0,W28,D10,L1,V0,M1} { hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ),
% 19.99/20.35 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 19.99/20.35 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 19.99/20.35 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 19.99/20.35 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 19.99/20.35 tc_Complex_Ocomplex ) ) ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex,
% 19.99/20.35 v_a____, v_pa____ ) ) ), v_pa____ ) ) }.
% 19.99/20.35 (81348) {G0,W29,D10,L1,V0,M1} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ),
% 19.99/20.35 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 19.99/20.35 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 19.99/20.35 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 19.99/20.35 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 19.99/20.35 tc_Complex_Ocomplex ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder(
% 19.99/20.35 tc_Complex_Ocomplex, v_a____, v_pa____ ) ) ) ), v_pa____ ) ) }.
% 19.99/20.35 (81349) {G0,W8,D3,L2,V1,M2} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 19.99/20.35 (81350) {G0,W8,D3,L2,V1,M2} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 19.99/20.35 (81351) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Olinordered__ring( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Ozero__class_Ozero
% 19.99/20.35 ( X ) ) }.
% 19.99/20.35 (81352) {G0,W8,D3,L2,V1,M2} { ! class_Rings_Olinordered__semidom( X ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 19.99/20.35 c_Groups_Oone__class_Oone( X ) ) }.
% 19.99/20.35 (81353) {G0,W8,D3,L2,V1,M2} { ! class_Rings_Olinordered__semidom( X ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 19.99/20.35 c_Groups_Oone__class_Oone( X ) ) }.
% 19.99/20.35 (81354) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Olinordered__ring( X ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 19.99/20.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 19.99/20.35 (81355) {G0,W20,D5,L4,V3,M4} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha2(
% 19.99/20.35 X, Y, Z ), alpha14( X, Y, Z ) }.
% 19.99/20.35 (81356) {G0,W16,D5,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 19.99/20.35 (81357) {G0,W16,D5,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 19.99/20.35 (81358) {G0,W9,D3,L2,V3,M2} { ! alpha14( X, Y, Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 ) }.
% 19.99/20.35 (81359) {G0,W9,D3,L2,V3,M2} { ! alpha14( X, Y, Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 ) }.
% 19.99/20.35 (81360) {G0,W14,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 X, Y, c_Groups_Ozero__class_Ozero( X ) ), alpha14( X, Y, Z ) }.
% 19.99/20.35 (81361) {G0,W9,D3,L2,V3,M2} { ! alpha2( X, Y, Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 19.99/20.35 ) }.
% 19.99/20.35 (81362) {G0,W9,D3,L2,V3,M2} { ! alpha2( X, Y, Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 19.99/20.35 ) }.
% 19.99/20.35 (81363) {G0,W14,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 19.99/20.35 ), alpha2( X, Y, Z ) }.
% 19.99/20.35 (81364) {G0,W13,D3,L3,V2,M3} { ! class_Rings_Olinordered__idom( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 19.99/20.35 Y ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 X ) ) }.
% 19.99/20.35 (81365) {G0,W13,D3,L3,V2,M3} { ! class_Rings_Olinordered__idom( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 19.99/20.35 Y ) ) }.
% 19.99/20.35 (81366) {G0,W20,D5,L4,V3,M4} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 19.99/20.35 ( X ) ), alpha3( X, Y, Z ), alpha15( X, Y, Z ) }.
% 19.99/20.35 (81367) {G0,W16,D5,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP
% 19.99/20.35 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 19.99/20.35 (81368) {G0,W16,D5,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 19.99/20.35 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 19.99/20.35 (81369) {G0,W9,D3,L2,V3,M2} { ! alpha15( X, Y, Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 ) }.
% 19.99/20.35 (81370) {G0,W9,D3,L2,V3,M2} { ! alpha15( X, Y, Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 19.99/20.35 ) }.
% 19.99/20.35 (81371) {G0,W14,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 X, c_Groups_Ozero__class_Ozero( X ), Y ), alpha15( X, Y, Z ) }.
% 19.99/20.35 (81372) {G0,W9,D3,L2,V3,M2} { ! alpha3( X, Y, Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 19.99/20.35 ) }.
% 19.99/20.35 (81373) {G0,W9,D3,L2,V3,M2} { ! alpha3( X, Y, Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 ) }.
% 19.99/20.35 (81374) {G0,W14,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 ), alpha3( X, Y, Z ) }.
% 19.99/20.35 (81375) {G0,W26,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha4( X, Y, Z, T ),
% 19.99/20.35 alpha16( X, Y, Z, T ) }.
% 19.99/20.35 (81376) {G0,W21,D5,L3,V4,M3} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP
% 19.99/20.35 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 19.99/20.35 (81377) {G0,W21,D5,L3,V4,M3} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP
% 19.99/20.35 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 19.99/20.35 (81378) {G0,W10,D3,L2,V4,M2} { ! alpha16( X, Y, Z, T ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 19.99/20.35 }.
% 19.99/20.35 (81379) {G0,W9,D2,L2,V4,M2} { ! alpha16( X, Y, Z, T ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 19.99/20.35 (81380) {G0,W14,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless( X, Z,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X, Y
% 19.99/20.35 , T ), alpha16( X, Y, Z, T ) }.
% 19.99/20.35 (81381) {G0,W10,D3,L2,V4,M2} { ! alpha4( X, Y, Z, T ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 19.99/20.35 }.
% 19.99/20.35 (81382) {G0,W9,D2,L2,V4,M2} { ! alpha4( X, Y, Z, T ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 19.99/20.35 (81383) {G0,W14,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless( X,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless( X
% 19.99/20.35 , T, Y ), alpha4( X, Y, Z, T ) }.
% 19.99/20.35 (81384) {G0,W26,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha5( X, Y, Z, T ),
% 19.99/20.35 alpha17( X, Y, Z, T ) }.
% 19.99/20.35 (81385) {G0,W21,D5,L3,V4,M3} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP
% 19.99/20.35 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 19.99/20.35 (81386) {G0,W21,D5,L3,V4,M3} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! alpha17( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP
% 19.99/20.35 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 19.99/20.35 (81387) {G0,W10,D3,L2,V4,M2} { ! alpha17( X, Y, Z, T ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 19.99/20.35 }.
% 19.99/20.35 (81388) {G0,W9,D2,L2,V4,M2} { ! alpha17( X, Y, Z, T ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 19.99/20.35 (81389) {G0,W14,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless( X, T,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X, Y
% 19.99/20.35 , Z ), alpha17( X, Y, Z, T ) }.
% 19.99/20.35 (81390) {G0,W10,D3,L2,V4,M2} { ! alpha5( X, Y, Z, T ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 19.99/20.35 }.
% 19.99/20.35 (81391) {G0,W9,D2,L2,V4,M2} { ! alpha5( X, Y, Z, T ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 19.99/20.35 (81392) {G0,W14,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless( X,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 19.99/20.35 , Z, Y ), alpha5( X, Y, Z, T ) }.
% 19.99/20.35 (81393) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 , Y ), ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 19.99/20.35 (81394) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 19.99/20.35 (81395) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 19.99/20.35 (81396) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 19.99/20.35 (81397) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semiring__strict
% 19.99/20.35 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 19.99/20.35 ), Y ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 19.99/20.35 ( X ), Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 19.99/20.35 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 19.99/20.35 (81398) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__cancel__semiring( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 X ), Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 19.99/20.35 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 19.99/20.35 (81399) {G0,W26,D5,L5,V3,M5} { ! class_Rings_Olinordered__idom( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 X ), Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 19.99/20.35 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 19.99/20.35 (81400) {G0,W26,D5,L5,V3,M5} { ! class_Rings_Olinordered__idom( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 X ), Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 19.99/20.35 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 19.99/20.35 (81401) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semiring__strict
% 19.99/20.35 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 19.99/20.35 ), Y ), ! c_Orderings_Oord__class_Oless( X, Z,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 19.99/20.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 19.99/20.35 (81402) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semiring__strict
% 19.99/20.35 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 19.99/20.35 ), Y ), ! c_Orderings_Oord__class_Oless( X, Z,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 19.99/20.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 19.99/20.35 (81403) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__cancel__semiring( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 X ), Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 19.99/20.35 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 19.99/20.35 (81404) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__cancel__semiring( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 X ), Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 19.99/20.35 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 19.99/20.35 (81405) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semiring__strict
% 19.99/20.35 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 19.99/20.35 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 19.99/20.35 }.
% 19.99/20.35 (81406) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semiring__strict
% 19.99/20.35 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 19.99/20.35 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 19.99/20.35 }.
% 19.99/20.35 (81407) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 19.99/20.35 ) ), ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 19.99/20.35 (81408) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 19.99/20.35 ) ), ! c_Orderings_Oord__class_Oless( X, Z, T ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 19.99/20.35 (81409) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 19.99/20.35 ) ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 19.99/20.35 (81410) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 19.99/20.35 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 19.99/20.35 (81411) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semiring__strict
% 19.99/20.35 ( X ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero
% 19.99/20.35 ( X ) ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 19.99/20.35 ( X ), Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 19.99/20.35 ( X ) ) }.
% 19.99/20.35 (81412) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__cancel__semiring( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 19.99/20.35 ( X ) ) }.
% 19.99/20.35 (81413) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 19.99/20.35 ) ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero
% 19.99/20.35 ( X ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 19.99/20.35 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 19.99/20.35 (81414) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__ring( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 19.99/20.35 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 19.99/20.35 (81415) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring__strict
% 19.99/20.35 ( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 19.99/20.35 (81416) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring__strict
% 19.99/20.35 ( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 19.99/20.35 (81417) {G0,W25,D5,L4,V4,M4} { !
% 19.99/20.35 class_Rings_Olinordered__comm__semiring__strict( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 19.99/20.35 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 19.99/20.35 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 19.99/20.35 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 19.99/20.35 (81418) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Oordered__semiring( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 19.99/20.35 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 19.99/20.35 (81419) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Oordered__semiring( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 19.99/20.35 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 19.99/20.35 (81420) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Oordered__comm__semiring( X )
% 19.99/20.35 , ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 19.99/20.35 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 19.99/20.35 (81421) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 19.99/20.35 (81422) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 19.99/20.35 (81423) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Oordered__ring( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 19.99/20.35 (81424) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Oordered__ring( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 19.99/20.35 (81425) {G0,W34,D5,L6,V5,M6} { ! class_Rings_Olinordered__semiring__strict
% 19.99/20.35 ( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 19.99/20.35 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 19.99/20.35 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 19.99/20.35 (81426) {G0,W34,D5,L6,V5,M6} { ! class_Rings_Olinordered__semiring__strict
% 19.99/20.35 ( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, U, T ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 X ), U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 19.99/20.35 (81427) {G0,W34,D5,L6,V5,M6} { ! class_Rings_Olinordered__semiring__strict
% 19.99/20.35 ( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 19.99/20.35 (81428) {G0,W34,D5,L6,V5,M6} { ! class_Rings_Olinordered__semiring__strict
% 19.99/20.35 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 19.99/20.35 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 19.99/20.35 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 19.99/20.35 (81429) {G0,W34,D5,L6,V5,M6} { ! class_Rings_Oordered__semiring( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 19.99/20.35 (81430) {G0,W34,D5,L6,V5,M6} { ! class_Rings_Oordered__semiring( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 19.99/20.35 (81431) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 19.99/20.35 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 19.99/20.35 (81432) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring__strict
% 19.99/20.35 ( X ), ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 19.99/20.35 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 19.99/20.35 (81433) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 19.99/20.35 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 19.99/20.35 (81434) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring__strict
% 19.99/20.35 ( X ), ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 19.99/20.35 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 19.99/20.35 (81435) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring__strict
% 19.99/20.35 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 19.99/20.35 (81436) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semiring__strict
% 19.99/20.35 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 19.99/20.35 (81437) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__ring( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 X ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 19.99/20.35 (81438) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__ring( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 19.99/20.35 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 19.99/20.35 (81439) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__cancel__semiring( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 X ), Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 19.99/20.35 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 19.99/20.35 (81440) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Oordered__cancel__semiring( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 19.99/20.35 ( X ) ) }.
% 19.99/20.35 (81441) {G0,W19,D6,L2,V3,M2} { ! class_Rings_Oring( X ),
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 19.99/20.35 ( X, Y ) ) }.
% 19.99/20.35 (81442) {G0,W19,D6,L2,V3,M2} { ! class_Rings_Oring( X ),
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 19.99/20.35 ) ), Y ) }.
% 19.99/20.35 (81443) {G0,W19,D5,L2,V3,M2} { ! class_Rings_Oring( X ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 19.99/20.35 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 19.99/20.35 (81444) {G0,W19,D5,L2,V3,M2} { ! class_Rings_Oring( X ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 19.99/20.35 ) ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 19.99/20.35 (81445) {G0,W21,D5,L4,V2,M4} { ! class_Rings_Oring__1__no__zero__divisors
% 19.99/20.35 ( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 19.99/20.35 c_Groups_Oone__class_Oone( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 19.99/20.35 (81446) {G0,W15,D5,L3,V2,M3} { ! class_Rings_Oring__1__no__zero__divisors
% 19.99/20.35 ( X ), ! Y = c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 19.99/20.35 ( X ) }.
% 19.99/20.35 (81447) {G0,W17,D5,L3,V2,M3} { ! class_Rings_Oring__1__no__zero__divisors
% 19.99/20.35 ( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X,
% 19.99/20.35 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 19.99/20.35 ( X ) }.
% 19.99/20.35 (81448) {G0,W23,D5,L4,V3,M4} { ! class_Rings_Oidom( X ), ! hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Y ), Z = Y, Z =
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 19.99/20.35 (81449) {G0,W18,D5,L3,V3,M3} { ! class_Rings_Oidom( X ), ! Z = Y, hAPP(
% 19.99/20.35 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 19.99/20.35 (81450) {G0,W20,D5,L3,V3,M3} { ! class_Rings_Oidom( X ), ! Z =
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Y ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 19.99/20.35 (81451) {G0,W13,D2,L4,V3,M4} { ! class_Rings_Olinordered__idom( X ), Z = Y
% 19.99/20.35 , c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless
% 19.99/20.35 ( X, Y, Z ) }.
% 19.99/20.35 (81452) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 19.99/20.35 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 19.99/20.35 (81453) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 19.99/20.35 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 19.99/20.35 (81454) {G0,W25,D7,L2,V4,M2} { ! class_Groups_Oab__semigroup__mult( X ),
% 19.99/20.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 19.99/20.35 (81455) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 19.99/20.35 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 19.99/20.35 (81456) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 19.99/20.35 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 19.99/20.35 (81457) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus(
% 19.99/20.35 X, Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 19.99/20.35 (81458) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 19.99/20.35 , c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 19.99/20.35 (81459) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), !
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 19.99/20.35 ( X, Y ), Z = Y }.
% 19.99/20.35 (81460) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), ! Z = Y,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 19.99/20.35 ( X, Y ) }.
% 19.99/20.35 (81461) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 19.99/20.35 , Y ), Z ) }.
% 19.99/20.35 (81462) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 19.99/20.35 , Z ), Y ) }.
% 19.99/20.35 (81463) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus(
% 19.99/20.35 X, Z ), Y ), c_Orderings_Oord__class_Oless( X,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 19.99/20.35 (81464) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus(
% 19.99/20.35 X, Y ), Z ), c_Orderings_Oord__class_Oless( X,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 19.99/20.35 (81465) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), !
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Z ) = Y,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 19.99/20.35 (81466) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), !
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Y ) = Z,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 19.99/20.35 (81467) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 19.99/20.35 ( X, Z ) ) }.
% 19.99/20.35 (81468) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 19.99/20.35 ( X, Y ) ) }.
% 19.99/20.35 (81469) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, Z,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 19.99/20.35 ( X, Y, c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 19.99/20.35 (81470) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, Y,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Z ) ), c_Orderings_Oord__class_Oless
% 19.99/20.35 ( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 19.99/20.35 (81471) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), ! Z =
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Y ), Y =
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 19.99/20.35 (81472) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), ! Y =
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Z ), Z =
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 19.99/20.35 (81473) {G0,W11,D5,L2,V2,M2} { ! class_Groups_Ocomm__monoid__mult( X ),
% 19.99/20.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 19.99/20.35 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 19.99/20.35 (81474) {G0,W11,D5,L2,V2,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 19.99/20.35 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone
% 19.99/20.35 ( X ) ) = Y }.
% 19.99/20.35 (81475) {G0,W10,D3,L3,V2,M3} { ! class_Groups_Oone( X ), !
% 19.99/20.35 c_Groups_Oone__class_Oone( X ) = Y, Y = c_Groups_Oone__class_Oone( X )
% 19.99/20.35 }.
% 19.99/20.35 (81476) {G0,W10,D3,L3,V2,M3} { ! class_Groups_Oone( X ), ! Y =
% 19.99/20.35 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) = Y }.
% 19.99/20.35 (81477) {G0,W11,D5,L2,V2,M2} { ! class_Groups_Ocomm__monoid__mult( X ),
% 19.99/20.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone
% 19.99/20.35 ( X ) ), Y ) = Y }.
% 19.99/20.35 (81478) {G0,W11,D5,L2,V2,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 19.99/20.35 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X )
% 19.99/20.35 ), Y ) = Y }.
% 19.99/20.35 (81479) {G0,W9,D4,L2,V2,M2} { ! class_Groups_Ogroup__add( X ),
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 19.99/20.35 ) ) = Y }.
% 19.99/20.35 (81480) {G0,W14,D3,L3,V2,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 19.99/20.35 }.
% 19.99/20.35 (81481) {G0,W14,D3,L3,V2,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 19.99/20.35 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 , c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 19.99/20.35 (81482) {G0,W14,D3,L3,V2,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus(
% 19.99/20.35 X, Y ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 19.99/20.35 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 19.99/20.35 (81483) {G0,W14,D3,L3,V2,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 19.99/20.35 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 19.99/20.35 (81484) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 19.99/20.35 ( X ), ! c_Orderings_Oord__class_Oless( X,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 19.99/20.35 }.
% 19.99/20.35 (81485) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 19.99/20.35 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 19.99/20.35 ), Y ), c_Orderings_Oord__class_Oless( X,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) }.
% 19.99/20.35 (81486) {G0,W14,D3,L3,V2,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 X ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 ) }.
% 19.99/20.35 (81487) {G0,W14,D3,L3,V2,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 19.99/20.35 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 19.99/20.35 ) ) }.
% 19.99/20.35 (81488) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 19.99/20.35 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 ) }.
% 19.99/20.35 (81489) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 19.99/20.35 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 19.99/20.35 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 19.99/20.35 (81490) {G0,W14,D3,L3,V2,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 19.99/20.35 ), Y ) }.
% 19.99/20.35 (81491) {G0,W14,D3,L3,V2,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 X ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 ) }.
% 19.99/20.35 (81492) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 19.99/20.35 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 19.99/20.35 ) }.
% 19.99/20.35 (81493) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 19.99/20.35 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 19.99/20.35 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) }.
% 19.99/20.35 (81494) {G0,W33,D8,L2,V4,M2} { ! class_Rings_Ocomm__ring__1( X ), hAPP(
% 19.99/20.35 c_Polynomial_Opoly( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ), c_Polynomial_Omonom( X,
% 19.99/20.35 c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y ) = hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 19.99/20.35 X, Z ), Y ) ) }.
% 19.99/20.35 (81495) {G0,W19,D5,L2,V3,M2} { ! class_Groups_Oab__group__add( X ),
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 19.99/20.35 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 19.99/20.35 ( tc_Polynomial_Opoly( X ), Y ) ) }.
% 19.99/20.35 (81496) {G0,W19,D5,L2,V3,M2} { ! class_Groups_Oab__group__add( X ),
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 19.99/20.35 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 19.99/20.35 ( tc_Polynomial_Opoly( X ), Y ) ) }.
% 19.99/20.35 (81497) {G0,W18,D6,L2,V3,M2} { ! class_Rings_Ocomm__ring( X ), hAPP(
% 19.99/20.35 c_Polynomial_Opoly( X, c_Groups_Ouminus__class_Ouminus(
% 19.99/20.35 tc_Polynomial_Opoly( X ), Z ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X
% 19.99/20.35 , hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 19.99/20.35 (81498) {G0,W18,D6,L2,V3,M2} { ! class_Groups_Oab__group__add( X ), hAPP(
% 19.99/20.35 c_Polynomial_Ocoeff( X, c_Groups_Ouminus__class_Ouminus(
% 19.99/20.35 tc_Polynomial_Opoly( X ), Z ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X
% 19.99/20.35 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 19.99/20.35 (81499) {G0,W16,D4,L2,V3,M2} { ! class_Rings_Ocomm__ring( X ),
% 19.99/20.35 c_Polynomial_Osmult( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 19.99/20.35 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 19.99/20.35 (81500) {G0,W24,D8,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.35 ( c_Polynomial_Opoly( X, hAPP( hAPP( c_Power_Opower__class_Opower(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ), T ), Z ) ), Y ) = hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), hAPP( c_Polynomial_Opoly( X, T ), Y )
% 19.99/20.35 ), Z ) }.
% 19.99/20.35 (81501) {G0,W19,D5,L4,V3,M4} { ! class_Rings_Ono__zero__divisors( X ), !
% 19.99/20.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 19.99/20.35 = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81502) {G0,W19,D5,L4,V3,M4} { ! class_Rings_Ono__zero__divisors( X ), Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 19.99/20.35 ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81503) {G0,W19,D5,L4,V3,M4} { ! class_Rings_Oring__no__zero__divisors( X
% 19.99/20.35 ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 19.99/20.35 = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81504) {G0,W15,D5,L3,V3,M3} { ! class_Rings_Oring__no__zero__divisors( X
% 19.99/20.35 ), ! Z = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81505) {G0,W15,D5,L3,V3,M3} { ! class_Rings_Oring__no__zero__divisors( X
% 19.99/20.35 ), ! Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81506) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Omult__zero( X ), hAPP( hAPP
% 19.99/20.35 ( c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X
% 19.99/20.35 ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81507) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Omult__zero( X ), hAPP( hAPP
% 19.99/20.35 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) )
% 19.99/20.35 , Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81508) {G0,W7,D3,L2,V1,M2} { ! class_Rings_Ozero__neq__one( X ), !
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oone__class_Oone( X ) }.
% 19.99/20.35 (81509) {G0,W7,D3,L2,V1,M2} { ! class_Rings_Ozero__neq__one( X ), !
% 19.99/20.35 c_Groups_Oone__class_Oone( X ) = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81510) {G0,W28,D8,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 19.99/20.35 ( c_Polynomial_Opoly( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ), T ), Z ) ), Y ) = hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Opoly( X, T ), Y )
% 19.99/20.35 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 19.99/20.35 (81511) {G0,W18,D5,L3,V3,M3} { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL
% 19.99/20.35 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ),
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 19.99/20.35 (81512) {G0,W18,D5,L3,V3,M3} { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL
% 19.99/20.35 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP(
% 19.99/20.35 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 19.99/20.35 ( X, Y ) ) ) }.
% 19.99/20.35 (81513) {G0,W18,D5,L3,V3,M3} { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL
% 19.99/20.35 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ),
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 19.99/20.35 (81514) {G0,W18,D5,L3,V3,M3} { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL
% 19.99/20.35 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP(
% 19.99/20.35 hAPP( c_Rings_Odvd__class_Odvd( X ), c_Groups_Ouminus__class_Ouminus( X,
% 19.99/20.35 Z ) ), Y ) ) }.
% 19.99/20.35 (81515) {G0,W12,D6,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.35 ( c_Polynomial_Opoly( X, c_Groups_Oone__class_Oone( tc_Polynomial_Opoly(
% 19.99/20.35 X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 19.99/20.35 (81516) {G0,W16,D4,L2,V3,M2} { ! class_Groups_Oab__group__add( X ),
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 19.99/20.35 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 19.99/20.35 (81517) {G0,W14,D6,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.35 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 19.99/20.35 (81518) {G0,W14,D6,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.35 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 19.99/20.35 (81519) {G0,W21,D6,L3,V4,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 19.99/20.35 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP
% 19.99/20.35 ( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 19.99/20.35 (81520) {G0,W21,D6,L3,V4,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 19.99/20.35 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP
% 19.99/20.35 ( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 19.99/20.35 (81521) {G0,W33,D7,L4,V5,M4} { ! class_Rings_Ocomm__semiring__1( X ), !
% 19.99/20.35 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL(
% 19.99/20.35 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), U ), T ) ), hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 19.99/20.35 (81522) {G0,W17,D5,L3,V4,M3} { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( X ), Y ), Z ) ) }.
% 19.99/20.35 (81523) {G0,W21,D7,L3,V4,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 19.99/20.35 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), Y ) ), hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 19.99/20.35 (81524) {G0,W21,D7,L3,V4,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 19.99/20.35 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) ), hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 19.99/20.35 (81525) {G0,W10,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.35 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ),
% 19.99/20.35 c_Groups_Oone__class_Oone( X ) ), Y ) ) }.
% 19.99/20.35 (81526) {G0,W35,D10,L3,V3,M3} { ! class_Rings_Oidom( X ), Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hBOOL( hAPP(
% 19.99/20.35 hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 19.99/20.35 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 19.99/20.35 c_Polynomial_Oorder( X, Z, Y ) ) ), Y ) ) }.
% 19.99/20.35 (81527) {G0,W36,D10,L3,V3,M3} { ! class_Rings_Oidom( X ), Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP(
% 19.99/20.35 hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 19.99/20.35 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc
% 19.99/20.35 ( c_Polynomial_Oorder( X, Z, Y ) ) ) ), Y ) ) }.
% 19.99/20.35 (81528) {G0,W36,D10,L3,V3,M3} { ! class_Rings_Oidom( X ), Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP(
% 19.99/20.35 hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 19.99/20.35 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc
% 19.99/20.35 ( c_Polynomial_Oorder( X, Z, Y ) ) ) ), Y ) ) }.
% 19.99/20.35 (81529) {G0,W13,D5,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.35 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) =
% 19.99/20.35 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 19.99/20.35 (81530) {G0,W11,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 19.99/20.35 ( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81531) {G0,W11,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 19.99/20.35 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y }.
% 19.99/20.35 (81532) {G0,W12,D3,L3,V2,M3} { ! class_Groups_Ogroup__add( X ), !
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 19.99/20.35 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81533) {G0,W12,D3,L3,V2,M3} { ! class_Groups_Ogroup__add( X ), ! Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 19.99/20.35 = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81534) {G0,W11,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 19.99/20.35 ( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X, Y ), Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81535) {G0,W11,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 19.99/20.35 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Y =
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 19.99/20.35 (81536) {G0,W12,D3,L3,V2,M3} { ! class_Groups_Ogroup__add( X ), !
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 19.99/20.35 ), c_Groups_Ozero__class_Ozero( X ) = Y }.
% 19.99/20.35 (81537) {G0,W12,D3,L3,V2,M3} { ! class_Groups_Ogroup__add( X ), !
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) = Y, c_Groups_Ozero__class_Ozero( X ) =
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 19.99/20.35 (81538) {G0,W9,D4,L2,V1,M2} { ! class_Groups_Ogroup__add( X ),
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81539) {G0,W14,D4,L2,V3,M2} { ! class_Groups_Ozero( X ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 19.99/20.35 c_Polynomial_OpCons( X, Z, Y ) ), c_Nat_OSuc( c_Polynomial_Odegree( X, Y
% 19.99/20.35 ) ) ) }.
% 19.99/20.35 (81540) {G0,W22,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.35 ( c_Polynomial_Opoly( X, c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP(
% 19.99/20.35 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 19.99/20.35 (81541) {G0,W15,D6,L2,V2,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 19.99/20.35 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81542) {G0,W15,D6,L2,V2,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 19.99/20.35 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81543) {G0,W19,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.35 c_Polynomial_Osmult( X, T, c_Polynomial_Osmult( X, Z, Y ) ) =
% 19.99/20.35 c_Polynomial_Osmult( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T
% 19.99/20.35 ), Z ), Y ) }.
% 19.99/20.35 (81544) {G0,W23,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 19.99/20.35 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 19.99/20.35 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 19.99/20.35 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) )
% 19.99/20.35 }.
% 19.99/20.35 (81545) {G0,W23,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 19.99/20.35 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 19.99/20.35 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 19.99/20.35 ) }.
% 19.99/20.35 (81546) {G0,W9,D4,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.35 c_Polynomial_Osmult( X, c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 19.99/20.35 (81547) {G0,W30,D7,L4,V4,M4} { ! class_Rings_Oidom( X ), ! hBOOL( hAPP(
% 19.99/20.35 hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), T =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 19.99/20.35 (81548) {G0,W23,D7,L3,V4,M3} { ! class_Rings_Oidom( X ), ! T =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.35 ( X ), T ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y
% 19.99/20.35 ) ) ) }.
% 19.99/20.35 (81549) {G0,W26,D7,L3,V4,M3} { ! class_Rings_Oidom( X ), ! hBOOL( hAPP(
% 19.99/20.35 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.35 ( X ), T ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y
% 19.99/20.35 ) ) ) }.
% 19.99/20.35 (81550) {G0,W30,D7,L4,V4,M4} { ! class_Rings_Oidom( X ), ! hBOOL( hAPP(
% 19.99/20.35 hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), Z =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( X ), T ), Y ) ) }.
% 19.99/20.35 (81551) {G0,W23,D7,L3,V4,M3} { ! class_Rings_Oidom( X ), ! Z =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.35 ( X ), T ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z
% 19.99/20.35 ) ) ) }.
% 19.99/20.35 (81552) {G0,W26,D7,L3,V4,M3} { ! class_Rings_Oidom( X ), ! hBOOL( hAPP(
% 19.99/20.35 hAPP( c_Rings_Odvd__class_Odvd( X ), T ), Y ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.35 ( X ), T ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z
% 19.99/20.35 ) ) ) }.
% 19.99/20.35 (81553) {G0,W30,D10,L2,V3,M2} { ! class_Rings_Oidom( X ), hBOOL( hAPP(
% 19.99/20.35 hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 19.99/20.35 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 19.99/20.35 c_Polynomial_Oorder( X, Z, Y ) ) ), Y ) ) }.
% 19.99/20.35 (81554) {G0,W16,D6,L3,V2,M3} { ! class_Rings_Ocomm__semiring__1( X ), ! Y
% 19.99/20.35 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff(
% 19.99/20.35 X, c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 19.99/20.35 c_Groups_Oone__class_Oone( X ) }.
% 19.99/20.35 (81555) {G0,W16,D6,L3,V2,M3} { ! class_Rings_Ocomm__semiring__1( X ), Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X
% 19.99/20.35 , c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81556) {G0,W22,D9,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.35 c_Polynomial_Odegree( X, hAPP( hAPP( c_Power_Opower__class_Opower(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X, Z,
% 19.99/20.35 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y
% 19.99/20.35 }.
% 19.99/20.35 (81557) {G0,W25,D10,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.35 hAPP( c_Polynomial_Ocoeff( X, hAPP( hAPP( c_Power_Opower__class_Opower(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X, Z,
% 19.99/20.35 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y )
% 19.99/20.35 = c_Groups_Oone__class_Oone( X ) }.
% 19.99/20.35 (81558) {G0,W27,D4,L5,V3,M5} { ! class_Groups_Ozero( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 19.99/20.35 Z ), Y ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.35 c_Polynomial_Odegree( X, Z ), Y ) }.
% 19.99/20.35 (81559) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.35 c_Polynomial_Osynthetic__div( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81560) {G0,W17,D5,L2,V4,M2} { ! class_Groups_Ozero( X ), hAPP(
% 19.99/20.35 c_Polynomial_Ocoeff( X, c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y )
% 19.99/20.35 ) = hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 19.99/20.35 (81561) {G0,W22,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.35 c_Polynomial_Osmult( X, T, c_Polynomial_OpCons( X, Z, Y ) ) =
% 19.99/20.35 c_Polynomial_OpCons( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T
% 19.99/20.35 ), Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 19.99/20.35 (81562) {G0,W21,D5,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 19.99/20.35 ( c_Polynomial_Opoly( X, c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP(
% 19.99/20.35 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly(
% 19.99/20.35 X, Z ), Y ) ) }.
% 19.99/20.35 (81563) {G0,W21,D5,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 19.99/20.35 ( c_Polynomial_Ocoeff( X, c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP(
% 19.99/20.35 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff
% 19.99/20.35 ( X, Z ), Y ) ) }.
% 19.99/20.35 (81564) {G0,W13,D4,L2,V3,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 19.99/20.35 c_Polynomial_Osmult( X, Z, Y ) ), c_Polynomial_Odegree( X, Y ) ) }.
% 19.99/20.35 (81565) {G0,W19,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.35 c_Polynomial_Osmult( X, T, c_Polynomial_Omonom( X, Z, Y ) ) =
% 19.99/20.35 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T
% 19.99/20.35 ), Z ), Y ) }.
% 19.99/20.35 (81566) {G0,W11,D4,L2,V3,M2} { ! class_Groups_Ozero( X ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 19.99/20.35 c_Polynomial_Omonom( X, Z, Y ) ), Y ) }.
% 19.99/20.35 (81567) {G0,W29,D8,L3,V3,M3} { ! class_Rings_Oidom( X ), ! hAPP(
% 19.99/20.35 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), hBOOL
% 19.99/20.35 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 19.99/20.35 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ) }.
% 19.99/20.35 (81568) {G0,W29,D8,L3,V3,M3} { ! class_Rings_Oidom( X ), ! hBOOL( hAPP(
% 19.99/20.35 hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 19.99/20.35 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ),
% 19.99/20.35 hAPP( c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 }.
% 19.99/20.35 (81569) {G0,W29,D8,L3,V3,M3} { ! class_Rings_Oidom( X ), ! hBOOL( hAPP(
% 19.99/20.35 hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 19.99/20.35 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), hAPP( c_Polynomial_Opoly( X, Y )
% 19.99/20.35 , c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero
% 19.99/20.35 ( X ) }.
% 19.99/20.35 (81570) {G0,W29,D8,L3,V3,M3} { ! class_Rings_Oidom( X ), ! hAPP(
% 19.99/20.35 c_Polynomial_Opoly( X, Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons
% 19.99/20.35 ( X, Z, c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) }.
% 19.99/20.35 (81571) {G0,W18,D4,L3,V3,M3} { ! class_Groups_Ozero( X ), Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Z, Y ) ) = c_Nat_OSuc(
% 19.99/20.35 c_Polynomial_Odegree( X, Y ) ) }.
% 19.99/20.35 (81572) {G0,W16,D4,L3,V3,M3} { ! class_Groups_Ozero( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 19.99/20.35 , Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81573) {G0,W16,D4,L3,V3,M3} { ! class_Groups_Ozero( X ), hAPP(
% 19.99/20.35 c_Polynomial_Ocoeff( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Polynomial_Odegree(
% 19.99/20.35 X, Z ) ) }.
% 19.99/20.35 (81574) {G0,W16,D4,L2,V3,M2} { ! class_Groups_Ozero( X ),
% 19.99/20.35 c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) = c_Polynomial_OpCons( X,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ), c_Polynomial_Omonom( X, Z, Y ) ) }.
% 19.99/20.35 (81575) {G0,W9,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ), hBOOL
% 19.99/20.35 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Y ) ) }.
% 19.99/20.35 (81576) {G0,W23,D5,L4,V4,M4} { ! class_Rings_Ocomm__semiring__1( X ), !
% 19.99/20.35 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL(
% 19.99/20.35 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 19.99/20.35 (81577) {G0,W23,D6,L4,V3,M4} { ! class_Rings_Oidom( X ), ! hBOOL( hAPP(
% 19.99/20.35 hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), Y
% 19.99/20.35 = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 19.99/20.35 Z ), c_Polynomial_Odegree( X, Y ) ) }.
% 19.99/20.35 (81578) {G0,W16,D4,L3,V3,M3} { ! class_Rings_Oidom( X ), Y =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Oorder( X, Z
% 19.99/20.35 , Y ), c_Polynomial_Odegree( X, Y ) ) }.
% 19.99/20.35 (81579) {G0,W29,D10,L1,V0,M1} { v_pa____ = hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.35 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 19.99/20.35 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 19.99/20.35 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 19.99/20.35 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 19.99/20.35 tc_Complex_Ocomplex ) ) ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex,
% 19.99/20.35 v_a____, v_pa____ ) ) ), skol4 ) }.
% 19.99/20.35 (81580) {G0,W20,D8,L1,V0,M1} { v_qa____ = hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.35 ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 19.99/20.35 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 19.99/20.35 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 19.99/20.35 tc_Complex_Ocomplex ) ) ) ) ), skol5 ) }.
% 19.99/20.35 (81581) {G0,W6,D3,L1,V1,M1} { c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 19.99/20.35 (81582) {G0,W30,D5,L5,V4,M5} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 19.99/20.35 (81583) {G0,W5,D3,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 19.99/20.35 (81584) {G0,W5,D3,L1,V1,M1} { c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.35 X, c_Nat_OSuc( X ) ) }.
% 19.99/20.35 (81585) {G0,W10,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.35 c_Nat_OSuc( Y ), c_Nat_OSuc( X ) ) }.
% 19.99/20.35 (81586) {G0,W5,D3,L1,V1,M1} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 19.99/20.35 (81587) {G0,W9,D6,L1,V1,M1} { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 19.99/20.35 ( tc_Nat_Onat ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 19.99/20.35 ), X ) ) }.
% 19.99/20.35 (81588) {G0,W19,D6,L3,V3,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ), Z ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y )
% 19.99/20.35 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 19.99/20.35 (81589) {G0,W18,D6,L3,V3,M3} { ! class_Rings_Ocomm__semiring__1( X ), ! Y
% 19.99/20.35 = c_Groups_Oone__class_Oone( X ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 19.99/20.35 (81590) {G0,W7,D5,L1,V1,M1} { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 19.99/20.35 ( tc_Nat_Onat ), X ), X ) ) }.
% 19.99/20.35 (81591) {G0,W16,D5,L3,V2,M3} { ! Y = hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 19.99/20.35 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Ozero__class_Ozero
% 19.99/20.35 ( tc_Nat_Onat ) }.
% 19.99/20.35 (81592) {G0,W28,D5,L4,V2,M4} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.35 (81593) {G0,W35,D5,L5,V3,M5} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z ) ), hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ), hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z ) ) }.
% 19.99/20.35 (81594) {G0,W35,D5,L5,V3,M5} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z ) ), hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ), ! hBOOL( hAPP(
% 19.99/20.35 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 19.99/20.35 (81595) {G0,W28,D5,L4,V2,M4} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.35 (81596) {G0,W28,D5,L4,V3,M4} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z ) ), hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z ) ) }.
% 19.99/20.35 (81597) {G0,W28,D5,L4,V3,M4} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z ) ), ! hBOOL( hAPP(
% 19.99/20.35 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 19.99/20.35 (81598) {G0,W24,D5,L4,V3,M4} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), ! X = Z, hBOOL( hAPP
% 19.99/20.35 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z ) ) }.
% 19.99/20.35 (81599) {G0,W24,D5,L4,V3,M4} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), ! X = Z, ! hBOOL(
% 19.99/20.35 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 19.99/20.35 (81600) {G0,W17,D5,L3,V2,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), ! X = Y }.
% 19.99/20.35 (81601) {G0,W17,D5,L3,V2,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), ! Y = X }.
% 19.99/20.35 (81602) {G0,W28,D5,L4,V2,M4} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.35 (81603) {G0,W21,D5,L3,V2,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.35 (81604) {G0,W28,D5,L4,V2,M4} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.35 (81605) {G0,W17,D5,L3,V2,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), ! Y = X }.
% 19.99/20.35 (81606) {G0,W28,D5,L4,V3,M4} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z ) ), hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ), hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z ) ) }.
% 19.99/20.35 (81607) {G0,W28,D5,L4,V3,M4} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z ) ), hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ), ! hBOOL( hAPP(
% 19.99/20.35 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 19.99/20.35 (81608) {G0,W24,D5,L4,V3,M4} { ! Y = X, ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z ) ) }.
% 19.99/20.35 (81609) {G0,W24,D5,L4,V3,M4} { ! Y = X, ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 19.99/20.35 (81610) {G0,W21,D5,L3,V3,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z ) ), hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z ) ) }.
% 19.99/20.35 (81611) {G0,W17,D5,L3,V2,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), Y = X }.
% 19.99/20.35 (81612) {G0,W17,D5,L3,V2,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), Y = X }.
% 19.99/20.35 (81613) {G0,W17,D5,L3,V3,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), ! X = Z, hBOOL( hAPP
% 19.99/20.35 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z ) ) }.
% 19.99/20.35 (81614) {G0,W17,D5,L3,V3,M3} { ! Y = X, ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z ) ) }.
% 19.99/20.35 (81615) {G0,W17,D5,L3,V2,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), Y = X, hBOOL( hAPP(
% 19.99/20.35 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.35 (81616) {G0,W17,D5,L3,V2,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), Y = X, ! hBOOL( hAPP
% 19.99/20.35 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ) }.
% 19.99/20.35 (81617) {G0,W17,D5,L3,V2,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), Y = X }.
% 19.99/20.35 (81618) {G0,W17,D5,L3,V2,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), Y = X }.
% 19.99/20.35 (81619) {G0,W17,D5,L3,V2,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), X = Y }.
% 19.99/20.35 (81620) {G0,W17,D5,L3,V2,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), ! X = Y, hBOOL( hAPP
% 19.99/20.35 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ) }.
% 19.99/20.35 (81621) {G0,W10,D5,L2,V2,M2} { ! Y = X, hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.35 (81622) {G0,W17,D5,L3,V2,M3} { Y = X, ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.35 (81623) {G0,W17,D5,L3,V2,M3} { Y = X, ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ) }.
% 19.99/20.35 (81624) {G0,W10,D5,L2,V2,M2} { ! alpha6( X, Y ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.35 (81625) {G0,W6,D2,L2,V2,M2} { ! alpha6( X, Y ), ! Y = X }.
% 19.99/20.35 (81626) {G0,W13,D5,L3,V2,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), Y = X, alpha6( X, Y
% 19.99/20.35 ) }.
% 19.99/20.35 (81627) {G0,W10,D5,L2,V2,M2} { ! alpha6( X, Y ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.35 (81628) {G0,W10,D5,L2,V2,M2} { ! alpha6( X, Y ), ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ) }.
% 19.99/20.35 (81629) {G0,W17,D5,L3,V2,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), alpha6( X, Y ) }.
% 19.99/20.35 (81630) {G0,W13,D5,L3,V2,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), alpha7( X, Y ), Y =
% 19.99/20.35 X }.
% 19.99/20.35 (81631) {G0,W10,D5,L2,V2,M2} { ! alpha7( X, Y ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.35 (81632) {G0,W10,D5,L2,V2,M2} { ! Y = X, hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.35 (81633) {G0,W10,D5,L2,V2,M2} { ! alpha7( X, Y ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.35 (81634) {G0,W10,D5,L2,V2,M2} { ! alpha7( X, Y ), ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ) }.
% 19.99/20.35 (81635) {G0,W17,D5,L3,V2,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), alpha7( X, Y ) }.
% 19.99/20.35 (81636) {G0,W10,D5,L2,V2,M2} { ! Y = X, hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.35 (81637) {G0,W10,D5,L2,V2,M2} { ! Y = X, hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ) }.
% 19.99/20.35 (81638) {G0,W17,D5,L3,V2,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) ), Y = X }.
% 19.99/20.35 (81639) {G0,W12,D5,L2,V1,M2} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone(
% 19.99/20.35 tc_Nat_Onat ) ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 19.99/20.35 (81640) {G0,W12,D5,L2,V1,M2} { ! X = c_Groups_Oone__class_Oone(
% 19.99/20.35 tc_Nat_Onat ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat )
% 19.99/20.35 , X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 19.99/20.35 (81641) {G0,W20,D5,L3,V3,M3} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.35 ( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.35 tc_Nat_Onat ), X ), Y ), Z = X, Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ) }.
% 19.99/20.35 (81642) {G0,W16,D5,L2,V3,M2} { ! Z = X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 19.99/20.35 (81643) {G0,W17,D5,L2,V3,M2} { ! Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 19.99/20.35 Z ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 19.99/20.35 , Y ) }.
% 19.99/20.35 (81644) {G0,W20,D5,L3,V3,M3} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.35 ( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.35 tc_Nat_Onat ), Z ), X ), Y = X, Z = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ) }.
% 19.99/20.35 (81645) {G0,W16,D5,L2,V3,M2} { ! Y = X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 19.99/20.35 (81646) {G0,W17,D5,L2,V3,M2} { ! Z = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 19.99/20.35 Z ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z )
% 19.99/20.35 , X ) }.
% 19.99/20.35 (81647) {G0,W17,D5,L3,V2,M3} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.35 ( tc_Nat_Onat ), Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y
% 19.99/20.35 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.35 (81648) {G0,W13,D5,L2,V2,M2} { ! Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 19.99/20.35 Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.35 (81649) {G0,W13,D5,L2,V2,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 19.99/20.35 Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.35 (81650) {G0,W10,D5,L1,V1,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.35 tc_Nat_Onat ), X ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.35 (81651) {G0,W10,D5,L1,V1,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.35 tc_Nat_Onat ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.35 (81652) {G0,W25,D7,L2,V4,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 19.99/20.35 hAPP( c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 19.99/20.35 (81653) {G0,W18,D5,L2,V3,M2} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.35 ( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ), Y =
% 19.99/20.35 X }.
% 19.99/20.35 (81654) {G0,W18,D5,L2,V3,M2} { ! Y = X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ) =
% 19.99/20.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 19.99/20.35 ), X ) }.
% 19.99/20.35 (81655) {G0,W11,D5,L2,V2,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 19.99/20.35 hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 19.99/20.35 tc_Nat_Onat ) ) = Y }.
% 19.99/20.35 (81656) {G0,W22,D5,L3,V4,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T
% 19.99/20.35 , Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 19.99/20.35 (81657) {G0,W18,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 19.99/20.35 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 19.99/20.35 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 19.99/20.35 (81658) {G0,W18,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 19.99/20.35 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP(
% 19.99/20.35 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 19.99/20.35 (81659) {G0,W14,D6,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 19.99/20.35 , X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X )
% 19.99/20.35 ) ) }.
% 19.99/20.35 (81660) {G0,W9,D5,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 19.99/20.35 , X ), X ) ) }.
% 19.99/20.35 (81661) {G0,W26,D7,L3,V3,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ) ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 19.99/20.35 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 19.99/20.35 ) }.
% 19.99/20.35 (81662) {G0,W21,D7,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! hBOOL(
% 19.99/20.35 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ), X ) ), Y =
% 19.99/20.35 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 19.99/20.35 (81663) {G0,W21,D7,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! Y =
% 19.99/20.35 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ), X ) ) }.
% 19.99/20.35 (81664) {G0,W21,D7,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! hBOOL(
% 19.99/20.35 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X ) ), Y =
% 19.99/20.35 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 19.99/20.35 (81665) {G0,W21,D7,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! Y =
% 19.99/20.35 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X ) ) }.
% 19.99/20.35 (81666) {G0,W12,D5,L2,V1,M2} { ! class_Groups_Oab__group__add( X ),
% 19.99/20.35 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.35 (81667) {G0,W12,D5,L2,V2,M2} { ! class_Groups_Oab__group__add( X ),
% 19.99/20.35 c_Polynomial_Odegree( X, c_Groups_Ouminus__class_Ouminus(
% 19.99/20.35 tc_Polynomial_Opoly( X ), Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 19.99/20.35 (81668) {G0,W17,D5,L2,V3,M2} { ! class_Rings_Ocomm__ring( X ),
% 19.99/20.35 c_Polynomial_Osmult( X, Z, c_Groups_Ouminus__class_Ouminus(
% 19.99/20.35 tc_Polynomial_Opoly( X ), Y ) ) = c_Groups_Ouminus__class_Ouminus(
% 19.99/20.35 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 19.99/20.35 (81669) {G0,W19,D5,L3,V2,M3} { ! hAPP( hAPP( c_Power_Opower__class_Opower
% 19.99/20.35 ( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 19.99/20.35 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 19.99/20.35 (81670) {G0,W14,D5,L2,V2,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 19.99/20.35 ), X ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 19.99/20.35 (81671) {G0,W15,D5,L2,V2,M2} { ! Y = c_Nat_OSuc(
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 19.99/20.35 (81672) {G0,W12,D6,L1,V1,M1} { hAPP( hAPP( c_Power_Opower__class_Opower(
% 19.99/20.35 tc_Nat_Onat ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) )
% 19.99/20.35 , X ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 19.99/20.35 (81673) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 19.99/20.35 (81674) {G0,W19,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ), Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.35 (81675) {G0,W15,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 19.99/20.35 ), X ) ) }.
% 19.99/20.35 (81676) {G0,W14,D5,L2,V2,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.35 (81677) {G0,W15,D5,L2,V2,M2} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.35 ( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ) ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 19.99/20.35 ) ) }.
% 19.99/20.35 (81678) {G0,W15,D5,L2,V2,M2} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.35 ( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ) ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 19.99/20.35 ) ) }.
% 19.99/20.35 (81679) {G0,W20,D5,L3,V2,M3} { ! Y = c_Nat_OSuc(
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X = c_Nat_OSuc(
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 19.99/20.35 (81680) {G0,W29,D7,L3,V3,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ), Z ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 19.99/20.35 tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.35 (81681) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 19.99/20.35 (81682) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 19.99/20.35 (81683) {G0,W19,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 19.99/20.35 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y
% 19.99/20.35 ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 19.99/20.35 (81684) {G0,W18,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 19.99/20.35 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y
% 19.99/20.35 ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 19.99/20.35 (81685) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 19.99/20.35 (81686) {G0,W19,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 19.99/20.35 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X
% 19.99/20.35 ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ) }.
% 19.99/20.35 (81687) {G0,W18,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 19.99/20.35 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X
% 19.99/20.35 ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 19.99/20.35 (81688) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 19.99/20.35 (81689) {G0,W15,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ), Y ) }.
% 19.99/20.35 (81690) {G0,W15,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ), X ) }.
% 19.99/20.35 (81691) {G0,W20,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.35 (81692) {G0,W20,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 19.99/20.35 c_Nat_OSuc( Z ) ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.35 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) ), c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, Y, X ) }.
% 19.99/20.35 (81693) {G0,W20,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 19.99/20.35 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y
% 19.99/20.35 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc
% 19.99/20.35 ( Z ) ), X ) ) }.
% 19.99/20.35 (81694) {G0,W20,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 19.99/20.35 c_Nat_OSuc( Z ) ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.35 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 19.99/20.35 (81695) {G0,W20,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 19.99/20.35 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ),
% 19.99/20.35 Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc
% 19.99/20.35 ( Z ) ), X ) ) }.
% 19.99/20.35 (81696) {G0,W6,D4,L1,V0,M1} { c_Groups_Oone__class_Oone( tc_Nat_Onat ) =
% 19.99/20.35 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 19.99/20.35 (81697) {G0,W17,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X
% 19.99/20.35 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 19.99/20.35 (81698) {G0,W23,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.35 (81699) {G0,W21,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 19.99/20.35 (81700) {G0,W21,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.35 (81701) {G0,W17,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 19.99/20.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 19.99/20.35 (81702) {G0,W17,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 19.99/20.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 19.99/20.35 (81703) {G0,W23,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.35 (81704) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 19.99/20.35 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y
% 19.99/20.35 ) ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 19.99/20.35 (81705) {G0,W19,D5,L2,V3,M2} { c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 19.99/20.35 (81706) {G0,W18,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Z, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 19.99/20.35 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 19.99/20.35 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 19.99/20.35 (81707) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 19.99/20.35 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X
% 19.99/20.35 ) ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 19.99/20.35 (81708) {G0,W19,D5,L2,V3,M2} { c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 19.99/20.35 (81709) {G0,W18,D5,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 19.99/20.35 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 19.99/20.35 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 19.99/20.35 (81710) {G0,W10,D5,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.35 c_Polynomial_Odegree( X, c_Groups_Oone__class_Oone( tc_Polynomial_Opoly(
% 19.99/20.35 X ) ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.35 (81711) {G0,W8,D3,L2,V2,M2} { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X
% 19.99/20.35 }.
% 19.99/20.35 (81712) {G0,W8,D3,L2,V2,M2} { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X
% 19.99/20.35 }.
% 19.99/20.35 (81713) {G0,W8,D3,L2,V2,M2} { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X )
% 19.99/20.35 }.
% 19.99/20.35 (81714) {G0,W4,D3,L1,V1,M1} { ! c_Nat_OSuc( X ) = X }.
% 19.99/20.35 (81715) {G0,W4,D3,L1,V1,M1} { ! X = c_Nat_OSuc( X ) }.
% 19.99/20.35 (81716) {G0,W14,D4,L3,V3,M3} { alpha23( X, Y, Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ), hBOOL( hAPP( hAPP( X
% 19.99/20.35 , Y ), Z ) ) }.
% 19.99/20.35 (81717) {G0,W16,D4,L3,V3,M3} { alpha23( X, Y, Z ), ! hBOOL( hAPP( hAPP( X
% 19.99/20.35 , Y ), Z ) ), hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 19.99/20.35 (81718) {G0,W11,D2,L3,V3,M3} { ! alpha23( X, Y, Z ), alpha25( X, Y, Z ), Z
% 19.99/20.35 = Y }.
% 19.99/20.35 (81719) {G0,W14,D4,L3,V3,M3} { ! alpha23( X, Y, Z ), alpha25( X, Y, Z ), !
% 19.99/20.35 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 19.99/20.35 (81720) {G0,W8,D2,L2,V3,M2} { ! alpha25( X, Y, Z ), alpha23( X, Y, Z ) }.
% 19.99/20.35 (81721) {G0,W13,D4,L3,V3,M3} { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ),
% 19.99/20.35 alpha23( X, Y, Z ) }.
% 19.99/20.35 (81722) {G0,W8,D2,L2,V3,M2} { ! alpha25( X, Y, Z ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 19.99/20.35 (81723) {G0,W10,D4,L2,V3,M2} { ! alpha25( X, Y, Z ), ! hBOOL( hAPP( hAPP(
% 19.99/20.35 X, Y ), Z ) ) }.
% 19.99/20.35 (81724) {G0,W14,D4,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha25( X, Y, Z )
% 19.99/20.35 }.
% 19.99/20.35 (81725) {G0,W7,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , Y, X ), ! Y = X }.
% 19.99/20.35 (81726) {G0,W7,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , Y, X ), ! X = Y }.
% 19.99/20.35 (81727) {G0,W4,D2,L1,V1,M1} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , X, X ) }.
% 19.99/20.35 (81728) {G0,W11,D2,L3,V2,M3} { Y = X, c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y )
% 19.99/20.35 }.
% 19.99/20.35 (81729) {G0,W11,D2,L3,V2,M3} { Y = X, c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y )
% 19.99/20.35 }.
% 19.99/20.35 (81730) {G0,W7,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , Y, X ), ! Y = X }.
% 19.99/20.35 (81731) {G0,W7,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , X, Y ), ! Y = X }.
% 19.99/20.35 (81732) {G0,W4,D2,L1,V1,M1} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , X, X ) }.
% 19.99/20.35 (81733) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 19.99/20.35 , Y ), Y = X }.
% 19.99/20.35 (81734) {G0,W12,D2,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 19.99/20.35 , Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 19.99/20.35 (81735) {G0,W7,D2,L2,V2,M2} { ! Y = X, c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ) }.
% 19.99/20.35 (81736) {G0,W8,D2,L2,V2,M2} { c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y
% 19.99/20.35 ) }.
% 19.99/20.35 (81737) {G0,W4,D2,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, X, X ) }.
% 19.99/20.35 (81738) {G0,W21,D7,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 19.99/20.35 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z )
% 19.99/20.35 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 19.99/20.35 c_Polynomial_Odegree( X, Z ) ), Y ) ) }.
% 19.99/20.35 (81739) {G0,W20,D5,L2,V3,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 19.99/20.35 c_Polynomial_Opcompose( X, Z, Y ) ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Polynomial_Odegree( X, Z
% 19.99/20.35 ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 19.99/20.35 (81740) {G0,W15,D5,L3,V3,M3} { ! class_Rings_Oring__1__no__zero__divisors
% 19.99/20.35 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 19.99/20.35 ( X ) }.
% 19.99/20.35 (81741) {G0,W30,D7,L2,V4,M2} { ! class_Groups_Ocomm__monoid__mult( X ),
% 19.99/20.35 hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 19.99/20.35 (81742) {G0,W25,D7,L2,V3,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 19.99/20.35 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 19.99/20.35 (81743) {G0,W12,D5,L2,V2,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 19.99/20.35 hAPP( c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) )
% 19.99/20.35 , Y ) = c_Groups_Oone__class_Oone( X ) }.
% 19.99/20.35 (81744) {G0,W5,D3,L1,V1,M1} { ! c_Nat_OSuc( X ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.35 (81745) {G0,W5,D3,L1,V1,M1} { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 19.99/20.35 = c_Nat_OSuc( X ) }.
% 19.99/20.35 (81746) {G0,W5,D3,L1,V1,M1} { ! c_Nat_OSuc( X ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.35 (81747) {G0,W5,D3,L1,V1,M1} { ! c_Nat_OSuc( X ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.35 (81748) {G0,W5,D3,L1,V1,M1} { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 19.99/20.35 = c_Nat_OSuc( X ) }.
% 19.99/20.35 (81749) {G0,W5,D3,L1,V1,M1} { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 19.99/20.35 = c_Nat_OSuc( X ) }.
% 19.99/20.35 (81750) {G0,W14,D5,L2,V1,M2} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Nat_OSuc(
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X = c_Nat_OSuc(
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 19.99/20.35 (81751) {G0,W14,D5,L2,V1,M2} { ! X = c_Nat_OSuc(
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Nat_OSuc(
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 19.99/20.35 (81752) {G0,W9,D3,L2,V1,M2} { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 19.99/20.35 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 19.99/20.35 (81753) {G0,W8,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , Y, X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.35 (81754) {G0,W5,D3,L1,V1,M1} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 19.99/20.35 (81755) {G0,W9,D3,L2,V1,M2} { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 19.99/20.35 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 19.99/20.35 (81756) {G0,W9,D3,L2,V1,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! X =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.35 (81757) {G0,W5,D3,L1,V1,M1} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 19.99/20.35 (81758) {G0,W16,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.35 (81759) {G0,W26,D7,L3,V4,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 19.99/20.35 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP
% 19.99/20.35 ( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Y ), T ) ) ) }.
% 19.99/20.35 (81760) {G0,W10,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc( X ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 19.99/20.35 (81761) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , c_Nat_OSuc( Y ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 19.99/20.35 ) }.
% 19.99/20.35 (81762) {G0,W12,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, Y, X ), Y = X }.
% 19.99/20.35 (81763) {G0,W13,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z )
% 19.99/20.35 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 19.99/20.35 (81764) {G0,W13,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X, c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 19.99/20.35 (81765) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X )
% 19.99/20.35 ) }.
% 19.99/20.35 (81766) {G0,W12,D3,L3,V2,M3} { c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X
% 19.99/20.35 ) ), X = Y }.
% 19.99/20.35 (81767) {G0,W12,D3,L3,V2,M3} { c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X
% 19.99/20.35 ) ), Y = X }.
% 19.99/20.35 (81768) {G0,W12,D3,L3,V2,M3} { c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , Y, X ), ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 19.99/20.35 c_Nat_OSuc( X ) ) }.
% 19.99/20.35 (81769) {G0,W10,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc( X ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 19.99/20.35 (81770) {G0,W10,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.35 c_Nat_OSuc( Y ), c_Nat_OSuc( X ) ) }.
% 19.99/20.35 (81771) {G0,W12,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, Y, X ), Y = X }.
% 19.99/20.35 (81772) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X )
% 19.99/20.35 ) }.
% 19.99/20.35 (81773) {G0,W8,D3,L2,V2,M2} { ! Y = X, c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 19.99/20.35 (81774) {G0,W9,D3,L2,V2,M2} { c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.35 Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) )
% 19.99/20.35 }.
% 19.99/20.35 (81775) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , X, c_Nat_OSuc( Y ) ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 19.99/20.35 X ) }.
% 19.99/20.35 (81776) {G0,W9,D3,L2,V1,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.35 (81777) {G0,W9,D3,L2,V1,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 19.99/20.35 (81778) {G0,W5,D3,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 19.99/20.35 (81779) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, c_Nat_OSuc( Y ), X ), c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ) }.
% 19.99/20.35 (81780) {G0,W13,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X ) }.
% 19.99/20.35 (81781) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 19.99/20.35 c_Nat_OSuc( X ) ) }.
% 19.99/20.35 (81782) {G0,W10,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc( X ) ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 19.99/20.35 (81783) {G0,W10,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 19.99/20.35 c_Nat_OSuc( Y ), c_Nat_OSuc( X ) ) }.
% 19.99/20.35 (81784) {G0,W13,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X ) }.
% 19.99/20.35 (81785) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 19.99/20.35 c_Nat_OSuc( X ) ) }.
% 19.99/20.35 (81786) {G0,W9,D3,L2,V2,M2} { ! Y = c_Nat_OSuc( X ),
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 19.99/20.35 (81787) {G0,W9,D3,L2,V2,M2} { c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 19.99/20.35 c_Nat_OSuc( X ), Y ) }.
% 19.99/20.35 (81788) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, c_Nat_OSuc( X ), Y ), ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ) }.
% 19.99/20.35 (81789) {G0,W5,D3,L1,V1,M1} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, c_Nat_OSuc( X ), X ) }.
% 19.99/20.35 (81790) {G0,W8,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 19.99/20.35 (81791) {G0,W7,D2,L2,V2,M2} { ! Y = X, c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ) }.
% 19.99/20.35 (81792) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ), Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 19.99/20.35 , X ) }.
% 19.99/20.35 (81793) {G0,W8,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 19.99/20.35 (81794) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 19.99/20.35 Y = X }.
% 19.99/20.35 (81795) {G0,W8,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 19.99/20.35 (81796) {G0,W7,D2,L2,V2,M2} { ! Y = X, c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ) }.
% 19.99/20.35 (81797) {G0,W8,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 19.99/20.35 (81798) {G0,W7,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , Y, X ), ! Y = X }.
% 19.99/20.35 (81799) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ), Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 19.99/20.35 , X ) }.
% 19.99/20.35 (81800) {G0,W9,D4,L1,V3,M1} { hAPP( c_Nat_Onat_Onat__case( Z, Y, X ),
% 19.99/20.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Y }.
% 19.99/20.35 (81801) {G0,W11,D4,L1,V4,M1} { hAPP( c_Nat_Onat_Onat__case( T, Z, Y ),
% 19.99/20.35 c_Nat_OSuc( X ) ) = hAPP( Y, X ) }.
% 19.99/20.35 (81802) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 19.99/20.35 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 19.99/20.35 (81803) {G0,W17,D5,L3,V3,M3} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 19.99/20.35 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 19.99/20.35 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 19.99/20.35 (81804) {G0,W17,D5,L3,V3,M3} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 19.99/20.35 ( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 19.99/20.35 (81805) {G0,W17,D5,L3,V3,M3} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 19.99/20.35 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 19.99/20.35 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 19.99/20.35 (81806) {G0,W21,D5,L6,V3,M6} { ! class_Power_Opower( X ), !
% 19.99/20.35 class_Rings_Omult__zero( X ), ! class_Rings_Ono__zero__divisors( X ), !
% 19.99/20.35 class_Rings_Ozero__neq__one( X ), ! hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 19.99/20.35 ( X ), Z = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81807) {G0,W21,D5,L6,V3,M6} { ! class_Power_Opower( X ), !
% 19.99/20.35 class_Rings_Omult__zero( X ), ! class_Rings_Ono__zero__divisors( X ), !
% 19.99/20.35 class_Rings_Ozero__neq__one( X ), ! hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 19.99/20.35 ( X ), ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.35 (81808) {G0,W25,D5,L7,V3,M7} { ! class_Power_Opower( X ), !
% 19.99/20.35 class_Rings_Omult__zero( X ), ! class_Rings_Ono__zero__divisors( X ), !
% 19.99/20.35 class_Rings_Ozero__neq__one( X ), ! Z = c_Groups_Ozero__class_Ozero( X )
% 19.99/20.35 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 19.99/20.35 ( X ) }.
% 19.99/20.35 (81809) {G0,W23,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 19.99/20.35 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 19.99/20.35 (81810) {G0,W23,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 19.99/20.35 T = Z, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP(
% 19.99/20.35 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 19.99/20.35 (81811) {G0,W15,D5,L3,V2,M3} { ! class_Power_Opower( X ), !
% 19.99/20.35 class_Rings_Osemiring__0( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 19.99/20.35 X ), c_Groups_Ozero__class_Ozero( X ) ), c_Nat_OSuc( Y ) ) =
% 19.99/20.35 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.35 (81812) {G0,W21,D7,L2,V3,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 19.99/20.35 hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP(
% 19.99/20.35 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 19.99/20.35 (81813) {G0,W21,D6,L2,V3,M2} { ! class_Power_Opower( X ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 19.99/20.35 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 19.99/20.35 (81814) {G0,W12,D5,L2,V2,M2} { ! class_Power_Opower( X ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 19.99/20.35 (81815) {G0,W12,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ), alpha8( X, Y ) }.
% 19.99/20.35 (81816) {G0,W9,D3,L2,V2,M2} { ! Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc
% 19.99/20.35 ( X ) ) }.
% 19.99/20.35 (81817) {G0,W8,D3,L2,V2,M2} { ! alpha8( X, Y ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 19.99/20.35 (81818) {G0,W9,D4,L2,V3,M2} { ! alpha8( X, Y ), Y = c_Nat_OSuc( skol6( Z,
% 19.99/20.35 Y ) ) }.
% 19.99/20.35 (81819) {G0,W9,D3,L2,V2,M2} { ! alpha8( X, Y ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol6( X, Y ), X ) }.
% 19.99/20.35 (81820) {G0,W11,D3,L3,V3,M3} { ! Y = c_Nat_OSuc( Z ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ), alpha8( X, Y ) }.
% 19.99/20.35 (81821) {G0,W10,D4,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 19.99/20.35 ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.35 (81822) {G0,W10,D4,L2,V1,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc
% 19.99/20.35 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 19.99/20.35 (81823) {G0,W10,D4,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), X =
% 19.99/20.35 c_Nat_OSuc( skol7( X ) ) }.
% 19.99/20.35 (81824) {G0,W9,D3,L2,V2,M2} { ! X = c_Nat_OSuc( Y ),
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ), X ) }.
% 19.99/20.35 (81825) {G0,W16,D5,L3,V2,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.35 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 19.99/20.35 ) }.
% 19.99/20.35 (81826) {G0,W23,D7,L3,V4,M3} { ! class_Rings_Ocomm__semiring__1( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 19.99/20.35 ( X ), T ), Z ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y
% 19.99/20.35 ) ) ) }.
% 19.99/20.35 (81827) {G0,W30,D7,L4,V5,M4} { ! class_Rings_Ocomm__semiring__1( X ), !
% 19.99/20.35 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ), hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 19.99/20.35 ( X ), Z ), U ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T
% 19.99/20.35 ) ) ) }.
% 19.99/20.35 (81828) {G0,W30,D7,L4,V5,M4} { ! class_Rings_Ocomm__semiring__1( X ), !
% 19.99/20.35 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ), hBOOL( hAPP( hAPP
% 19.99/20.35 ( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 19.99/20.35 ( X ), T ), U ) ), Y ) ) }.
% 19.99/20.35 (81829) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, c_Nat_OSuc( Y ), X ), c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, Y, X ) }.
% 19.99/20.35 (81830) {G0,W12,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 19.99/20.35 c_Nat_OSuc( Y ) ), X = Y }.
% 19.99/20.35 (81831) {G0,W12,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ), ! X = Y, c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , X, c_Nat_OSuc( Y ) ) }.
% 19.99/20.35 (81832) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y )
% 19.99/20.35 , X ) }.
% 19.99/20.35 (81833) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 19.99/20.35 c_Nat_OSuc( X ) ) }.
% 19.99/20.35 (81834) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, c_Nat_OSuc( Y ), X ), c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, Y, X ) }.
% 19.99/20.35 (81835) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y )
% 19.99/20.35 , X ) }.
% 19.99/20.35 (81836) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , Y, c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 19.99/20.35 , X ) }.
% 19.99/20.35 (81837) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 19.99/20.35 c_Nat_OSuc( X ) ) }.
% 19.99/20.35 (81838) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.35 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y )
% 19.99/20.35 , X ) }.
% 19.99/20.35 (81839) {G0,W9,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.35 tc_Nat_Onat, c_Nat_OSuc( Y ), X ), c_Orderings_Oord__class_Oless(
% 19.99/20.35 tc_Nat_Onat, Y, X ) }.
% 19.99/20.35 (81840) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 19.99/20.35 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 19.99/20.35 (81841) {G0,W30,D5,L5,V4,M5} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.35 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) =
% 19.99/20.35 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 19.99/20.35 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.35 X ), Y ), Z = Y }.
% 19.99/20.35 (81842) {G0,W27,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 19.99/20.35 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 19.99/20.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 19.99/20.36 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 19.99/20.36 (81843) {G0,W26,D6,L3,V3,M3} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 19.99/20.36 (81844) {G0,W22,D6,L3,V3,M3} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 19.99/20.36 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 19.99/20.36 (81845) {G0,W18,D5,L4,V2,M4} { ! class_Power_Opower( X ), !
% 19.99/20.36 class_Rings_Osemiring__0( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) ), Y ) = c_Groups_Oone__class_Oone( X )
% 19.99/20.36 }.
% 19.99/20.36 (81846) {G0,W18,D5,L4,V2,M4} { ! class_Power_Opower( X ), !
% 19.99/20.36 class_Rings_Osemiring__0( X ), Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) ), Y ) = c_Groups_Ozero__class_Ozero( X
% 19.99/20.36 ) }.
% 19.99/20.36 (81847) {G0,W18,D5,L3,V3,M3} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 19.99/20.36 hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 19.99/20.36 (81848) {G0,W30,D8,L2,V3,M2} { ! class_Rings_Oring__1( X ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 19.99/20.36 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 19.99/20.36 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 19.99/20.36 (81849) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), T ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 19.99/20.36 (81850) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 19.99/20.36 (81851) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 19.99/20.36 (81852) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 19.99/20.36 (81853) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 19.99/20.36 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 19.99/20.36 (81854) {G0,W31,D6,L4,V3,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 19.99/20.36 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 19.99/20.36 (81855) {G0,W23,D5,L4,V3,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 19.99/20.36 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 19.99/20.36 c_Groups_Oone__class_Oone( X ) ) }.
% 19.99/20.36 (81856) {G0,W30,D5,L5,V4,M5} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 19.99/20.36 ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Oone__class_Oone( X ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 19.99/20.36 (81857) {G0,W33,D5,L6,V4,M6} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.36 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 19.99/20.36 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 19.99/20.36 (81858) {G0,W30,D5,L5,V4,M5} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 19.99/20.36 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 19.99/20.36 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 19.99/20.36 (81859) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 19.99/20.36 (81860) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 19.99/20.36 (81861) {G0,W25,D5,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 19.99/20.36 (81862) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( X,
% 19.99/20.36 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 19.99/20.36 ( X ), Y ), Z ) ) }.
% 19.99/20.36 (81863) {G0,W22,D5,L4,V3,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 19.99/20.36 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 19.99/20.36 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 19.99/20.36 (81864) {G0,W29,D6,L4,V3,M4} { ! class_Rings_Oidom( X ), ! hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 19.99/20.36 (81865) {G0,W24,D6,L3,V3,M3} { ! class_Rings_Oidom( X ), ! Z = Y, hAPP(
% 19.99/20.36 hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 19.99/20.36 (81866) {G0,W26,D6,L3,V3,M3} { ! class_Rings_Oidom( X ), ! Z =
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, Y ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 19.99/20.36 (81867) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 19.99/20.36 (81868) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 19.99/20.36 (81869) {G0,W29,D7,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! hBOOL(
% 19.99/20.36 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 19.99/20.36 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 19.99/20.36 (81870) {G0,W29,D7,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! hBOOL(
% 19.99/20.36 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), hBOOL(
% 19.99/20.36 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 19.99/20.36 (81871) {G0,W17,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! hBOOL(
% 19.99/20.36 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Nat_Onat ), Y ) }.
% 19.99/20.36 (81872) {G0,W16,D5,L3,V1,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Nat_Onat ) ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 19.99/20.36 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 19.99/20.36 (81873) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.36 ( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone
% 19.99/20.36 ( X ) }.
% 19.99/20.36 (81874) {G0,W9,D5,L1,V1,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.36 tc_Nat_Onat ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 19.99/20.36 (81875) {G0,W13,D5,L2,V2,M2} { ! c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 19.99/20.36 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 19.99/20.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 19.99/20.36 (81876) {G0,W13,D5,L2,V2,M2} { ! c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 19.99/20.36 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 19.99/20.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 19.99/20.36 (81877) {G0,W17,D5,L3,V2,M3} { ! Y = c_Groups_Oone__class_Oone(
% 19.99/20.36 tc_Nat_Onat ), ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 19.99/20.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) }.
% 19.99/20.36 (81878) {G0,W9,D5,L1,V1,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.36 tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 19.99/20.36 (81879) {G0,W13,D5,L1,V2,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.36 tc_Nat_Onat ), Y ), X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.36 tc_Nat_Onat ), X ), Y ) }.
% 19.99/20.36 (81880) {G0,W13,D5,L2,V2,M2} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( tc_Nat_Onat ), Y ), X ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 19.99/20.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 19.99/20.36 (81881) {G0,W13,D5,L2,V2,M2} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( tc_Nat_Onat ), Y ), X ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ), X =
% 19.99/20.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 19.99/20.36 (81882) {G0,W17,D5,L3,V2,M3} { ! Y = c_Groups_Oone__class_Oone(
% 19.99/20.36 tc_Nat_Onat ), ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP
% 19.99/20.36 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 19.99/20.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 19.99/20.36 (81883) {G0,W23,D7,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.36 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 19.99/20.36 Z ), Y ) ), X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat
% 19.99/20.36 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X
% 19.99/20.36 ) ) }.
% 19.99/20.36 (81884) {G0,W15,D5,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 19.99/20.36 (81885) {G0,W25,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 19.99/20.36 (81886) {G0,W25,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 19.99/20.36 (81887) {G0,W25,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 19.99/20.36 (81888) {G0,W25,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 19.99/20.36 (81889) {G0,W35,D7,L2,V5,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 19.99/20.36 (81890) {G0,W35,D8,L2,V5,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 19.99/20.36 (81891) {G0,W35,D7,L2,V5,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 19.99/20.36 (81892) {G0,W20,D5,L3,V3,M3} { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.36 tc_Nat_Onat ), Z ), X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 19.99/20.36 Y = X }.
% 19.99/20.36 (81893) {G0,W17,D5,L2,V3,M2} { ! Z = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 19.99/20.36 Z ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z )
% 19.99/20.36 , X ) }.
% 19.99/20.36 (81894) {G0,W16,D5,L2,V3,M2} { ! Y = X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 19.99/20.36 (81895) {G0,W28,D7,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Nat_Onat ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint
% 19.99/20.36 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ),
% 19.99/20.36 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ),
% 19.99/20.36 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) )
% 19.99/20.36 }.
% 19.99/20.36 (81896) {G0,W28,D7,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Nat_Onat ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint
% 19.99/20.36 ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint
% 19.99/20.36 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ),
% 19.99/20.36 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ) }.
% 19.99/20.36 (81897) {G0,W28,D7,L3,V3,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ) }.
% 19.99/20.36 (81898) {G0,W11,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.36 ( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone
% 19.99/20.36 ( tc_Nat_Onat ) ) = Y }.
% 19.99/20.36 (81899) {G0,W25,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.36 ( hAPP( c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 19.99/20.36 (81900) {G0,W8,D5,L1,V1,M1} { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 19.99/20.36 ( tc_Nat_Onat ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 19.99/20.36 (81901) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (81902) {G0,W12,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero(
% 19.99/20.36 X ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (81903) {G0,W11,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X
% 19.99/20.36 ) ), Y ) = Y }.
% 19.99/20.36 (81904) {G0,W11,D5,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 19.99/20.36 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 19.99/20.36 (81905) {G0,W30,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.36 ( hAPP( c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 19.99/20.36 (81906) {G0,W21,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! hAPP(
% 19.99/20.36 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP
% 19.99/20.36 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = Y }.
% 19.99/20.36 (81907) {G0,W21,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), ! Z = Y,
% 19.99/20.36 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) = hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 19.99/20.36 (81908) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 19.99/20.36 (81909) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 19.99/20.36 (81910) {G0,W19,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ), X =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 19.99/20.36 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 19.99/20.36 (81911) {G0,W14,D5,L2,V2,M2} { ! X = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Nat_Onat ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.36 (81912) {G0,W15,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 19.99/20.36 ), X ) ) }.
% 19.99/20.36 (81913) {G0,W8,D5,L1,V1,M1} { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 19.99/20.36 ( tc_Nat_Onat ), X ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 19.99/20.36 (81914) {G0,W28,D7,L3,V3,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), Z =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.36 (81915) {G0,W21,D7,L2,V3,M2} { ! Z = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Nat_Onat ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat )
% 19.99/20.36 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ),
% 19.99/20.36 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) )
% 19.99/20.36 }.
% 19.99/20.36 (81916) {G0,W24,D7,L2,V3,M2} { ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 19.99/20.36 (81917) {G0,W28,D7,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Nat_Onat ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat
% 19.99/20.36 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ),
% 19.99/20.36 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ),
% 19.99/20.36 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) )
% 19.99/20.36 }.
% 19.99/20.36 (81918) {G0,W28,D7,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Nat_Onat ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat
% 19.99/20.36 ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat
% 19.99/20.36 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ),
% 19.99/20.36 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ) }.
% 19.99/20.36 (81919) {G0,W28,D7,L3,V3,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 19.99/20.36 (81920) {G0,W15,D6,L2,V2,M2} { ! class_Rings_Ocomm__ring__1( X ),
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, Y ) = hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X,
% 19.99/20.36 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 19.99/20.36 (81921) {G0,W21,D6,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.36 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 19.99/20.36 (81922) {G0,W21,D6,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 19.99/20.36 (81923) {G0,W21,D7,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 19.99/20.36 (81924) {G0,W6,D2,L2,V2,M2} { ! class_Orderings_Opreorder( X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, Y ) }.
% 19.99/20.36 (81925) {G0,W11,D4,L2,V1,M2} { ! class_Power_Opower( X ),
% 19.99/20.36 c_Power_Opower__class_Opower( X ) = c_Power_Opower_Opower( X,
% 19.99/20.36 c_Groups_Oone__class_Oone( X ), c_Groups_Otimes__class_Otimes( X ) ) }.
% 19.99/20.36 (81926) {G0,W38,D9,L2,V3,M2} { ! class_Rings_Ocomm__ring__1( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 19.99/20.36 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 19.99/20.36 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 19.99/20.36 c_Polynomial_Osynthetic__div( X, Y, Z ) ), c_Polynomial_OpCons( X, hAPP(
% 19.99/20.36 c_Polynomial_Opoly( X, Y ), Z ), c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 19.99/20.36 (81927) {G0,W8,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.36 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 19.99/20.36 (81928) {G0,W9,D4,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, c_Groups_Ozero__class_Ozero( X ), Y ) = Y
% 19.99/20.36 }.
% 19.99/20.36 (81929) {G0,W9,D4,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Ozero__class_Ozero( X ) ) = Y
% 19.99/20.36 }.
% 19.99/20.36 (81930) {G0,W12,D3,L3,V3,M3} { !
% 19.99/20.36 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 19.99/20.36 ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (81931) {G0,W12,D3,L3,V3,M3} { !
% 19.99/20.36 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 19.99/20.36 ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 19.99/20.36 (81932) {G0,W37,D6,L4,V5,M4} { !
% 19.99/20.36 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 19.99/20.36 ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 19.99/20.36 ), U = Z, T = Y }.
% 19.99/20.36 (81933) {G0,W34,D6,L3,V5,M3} { !
% 19.99/20.36 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 19.99/20.36 ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 19.99/20.36 ) }.
% 19.99/20.36 (81934) {G0,W34,D6,L3,V5,M3} { !
% 19.99/20.36 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 19.99/20.36 ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 19.99/20.36 ) }.
% 19.99/20.36 (81935) {G0,W26,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z )
% 19.99/20.36 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, T, Y ) ), Z ) }.
% 19.99/20.36 (81936) {G0,W26,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus(
% 19.99/20.36 X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 19.99/20.36 (81937) {G0,W37,D6,L4,V5,M4} { !
% 19.99/20.36 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 19.99/20.36 ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 19.99/20.36 ) }.
% 19.99/20.36 (81938) {G0,W34,D6,L3,V5,M3} { !
% 19.99/20.36 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 19.99/20.36 ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 19.99/20.36 ), ! U = T }.
% 19.99/20.36 (81939) {G0,W34,D6,L3,V5,M3} { !
% 19.99/20.36 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 19.99/20.36 ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 19.99/20.36 ), ! Z = Y }.
% 19.99/20.36 (81940) {G0,W26,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 19.99/20.36 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 19.99/20.36 (81941) {G0,W11,D3,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Z, Y ) = c_Groups_Oplus__class_Oplus( X,
% 19.99/20.36 Y, Z ) }.
% 19.99/20.36 (81942) {G0,W17,D4,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y )
% 19.99/20.36 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Oplus__class_Oplus( X, T
% 19.99/20.36 , Y ) ) }.
% 19.99/20.36 (81943) {G0,W17,D4,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y )
% 19.99/20.36 ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 19.99/20.36 ), Y ) }.
% 19.99/20.36 (81944) {G0,W17,D4,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y
% 19.99/20.36 ) = c_Groups_Oplus__class_Oplus( X, T, c_Groups_Oplus__class_Oplus( X, Z
% 19.99/20.36 , Y ) ) }.
% 19.99/20.36 (81945) {G0,W17,D4,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y
% 19.99/20.36 ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, T, Y
% 19.99/20.36 ), Z ) }.
% 19.99/20.36 (81946) {G0,W23,D4,L2,V5,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, U, T ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 19.99/20.36 , c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus( X
% 19.99/20.36 , T, Y ) ) }.
% 19.99/20.36 (81947) {G0,W9,D4,L2,V2,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Ozero__class_Ozero( X ) ) = Y
% 19.99/20.36 }.
% 19.99/20.36 (81948) {G0,W9,D4,L2,V2,M2} { ! class_Groups_Omonoid__add( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Ozero__class_Ozero( X ) ) = Y
% 19.99/20.36 }.
% 19.99/20.36 (81949) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 19.99/20.36 ( X ), ! c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus(
% 19.99/20.36 X, Y, Y ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (81950) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 19.99/20.36 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 19.99/20.36 }.
% 19.99/20.36 (81951) {G0,W9,D4,L2,V2,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, c_Groups_Ozero__class_Ozero( X ), Y ) = Y
% 19.99/20.36 }.
% 19.99/20.36 (81952) {G0,W9,D4,L2,V2,M2} { ! class_Groups_Omonoid__add( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, c_Groups_Ozero__class_Ozero( X ), Y ) = Y
% 19.99/20.36 }.
% 19.99/20.36 (81953) {G0,W16,D3,L3,V4,M3} { !
% 19.99/20.36 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 19.99/20.36 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 19.99/20.36 (81954) {G0,W16,D3,L3,V4,M3} { !
% 19.99/20.36 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 19.99/20.36 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 19.99/20.36 (81955) {G0,W20,D3,L4,V5,M4} { ! class_Groups_Oordered__ab__semigroup__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 19.99/20.36 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 19.99/20.36 (81956) {G0,W16,D3,L3,V4,M3} { ! class_Groups_Oordered__ab__semigroup__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 19.99/20.36 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 19.99/20.36 (81957) {G0,W16,D3,L3,V4,M3} { ! class_Groups_Oordered__ab__semigroup__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 19.99/20.36 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 19.99/20.36 (81958) {G0,W16,D3,L3,V4,M3} { !
% 19.99/20.36 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 19.99/20.36 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 19.99/20.36 (81959) {G0,W16,D3,L3,V4,M3} { !
% 19.99/20.36 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 19.99/20.36 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 19.99/20.36 (81960) {G0,W16,D3,L3,V4,M3} { !
% 19.99/20.36 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 19.99/20.36 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 19.99/20.36 (81961) {G0,W16,D3,L3,V4,M3} { !
% 19.99/20.36 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 19.99/20.36 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 19.99/20.36 (81962) {G0,W16,D3,L3,V4,M3} { !
% 19.99/20.36 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 19.99/20.36 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, Z, Y ) }.
% 19.99/20.36 (81963) {G0,W16,D3,L3,V4,M3} { !
% 19.99/20.36 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 19.99/20.36 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, Z, Y ) }.
% 19.99/20.36 (81964) {G0,W20,D3,L4,V5,M4} { !
% 19.99/20.36 class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 19.99/20.36 , T ) ) }.
% 19.99/20.36 (81965) {G0,W16,D3,L3,V4,M3} { !
% 19.99/20.36 class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 19.99/20.36 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 19.99/20.36 , T, Y ) ) }.
% 19.99/20.36 (81966) {G0,W16,D3,L3,V4,M3} { !
% 19.99/20.36 class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 19.99/20.36 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 19.99/20.36 , Y, T ) ) }.
% 19.99/20.36 (81967) {G0,W16,D3,L3,V4,M3} { !
% 19.99/20.36 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 19.99/20.36 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, Z, Y ) }.
% 19.99/20.36 (81968) {G0,W16,D3,L3,V4,M3} { !
% 19.99/20.36 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 19.99/20.36 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 19.99/20.36 , T, Y ) ) }.
% 19.99/20.36 (81969) {G0,W16,D3,L3,V4,M3} { !
% 19.99/20.36 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 19.99/20.36 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, T, Y ) }.
% 19.99/20.36 (81970) {G0,W16,D3,L3,V4,M3} { !
% 19.99/20.36 class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 19.99/20.36 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 19.99/20.36 , Y, Z ) ) }.
% 19.99/20.36 (81971) {G0,W26,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring( X ), hAPP(
% 19.99/20.36 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 19.99/20.36 , T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 19.99/20.36 (81972) {G0,W32,D7,L2,V5,M2} { ! class_Rings_Osemiring( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ) ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), c_Groups_Oplus__class_Oplus( X, U, Z ) ), T ), Y ) }.
% 19.99/20.36 (81973) {G0,W13,D4,L2,V3,M2} { ! class_Groups_Ogroup__add( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = Y }.
% 19.99/20.36 (81974) {G0,W13,D5,L2,V3,M2} { ! class_Groups_Ogroup__add( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Oplus__class_Oplus( X,
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) ) = Y }.
% 19.99/20.36 (81975) {G0,W17,D4,L2,V3,M2} { ! class_Groups_Ogroup__add( X ),
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 19.99/20.36 ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X
% 19.99/20.36 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 19.99/20.36 (81976) {G0,W17,D4,L2,V3,M2} { ! class_Groups_Oab__group__add( X ),
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 19.99/20.36 ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X
% 19.99/20.36 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 19.99/20.36 (81977) {G0,W26,D5,L4,V4,M4} { ! class_Rings_Ocomm__semiring__1( X ), !
% 19.99/20.36 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL(
% 19.99/20.36 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP
% 19.99/20.36 ( c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X, Y,
% 19.99/20.36 T ) ) ) }.
% 19.99/20.36 (81978) {G0,W11,D5,L2,V2,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 19.99/20.36 (81979) {G0,W11,D5,L2,V2,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 19.99/20.36 (81980) {G0,W17,D4,L2,V4,M2} { ! class_Groups_Oab__semigroup__add( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y
% 19.99/20.36 ) = c_Groups_Oplus__class_Oplus( X, T, c_Groups_Oplus__class_Oplus( X, Z
% 19.99/20.36 , Y ) ) }.
% 19.99/20.36 (81981) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ocancel__semigroup__add( X )
% 19.99/20.36 , ! c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus
% 19.99/20.36 ( X, T, Y ), Z = Y }.
% 19.99/20.36 (81982) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ocancel__semigroup__add( X )
% 19.99/20.36 , ! Z = Y, c_Groups_Oplus__class_Oplus( X, T, Z ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 19.99/20.36 (81983) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ocancel__semigroup__add( X )
% 19.99/20.36 , ! c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus
% 19.99/20.36 ( X, Y, Z ), T = Y }.
% 19.99/20.36 (81984) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ocancel__semigroup__add( X )
% 19.99/20.36 , ! T = Y, c_Groups_Oplus__class_Oplus( X, T, Z ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 19.99/20.36 (81985) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ocancel__semigroup__add( X )
% 19.99/20.36 , ! c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus
% 19.99/20.36 ( X, T, Y ), Z = Y }.
% 19.99/20.36 (81986) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ocancel__ab__semigroup__add
% 19.99/20.36 ( X ), ! c_Groups_Oplus__class_Oplus( X, T, Z ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, T, Y ), Z = Y }.
% 19.99/20.36 (81987) {G0,W14,D3,L3,V4,M3} { ! class_Groups_Ocancel__semigroup__add( X )
% 19.99/20.36 , ! c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus
% 19.99/20.36 ( X, Y, T ), Z = Y }.
% 19.99/20.36 (81988) {G0,W21,D4,L2,V4,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 19.99/20.36 c_Polynomial_Omonom( X, T, Z ), c_Polynomial_Omonom( X, Y, Z ) ) =
% 19.99/20.36 c_Polynomial_Omonom( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 19.99/20.36 (81989) {G0,W24,D6,L2,V4,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 19.99/20.36 hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Polynomial_Opoly( X ), T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X
% 19.99/20.36 , hAPP( c_Polynomial_Ocoeff( X, T ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z
% 19.99/20.36 ), Y ) ) }.
% 19.99/20.36 (81990) {G0,W21,D4,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.36 c_Polynomial_Osmult( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 19.99/20.36 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 19.99/20.36 (81991) {G0,W24,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 19.99/20.36 ( c_Polynomial_Opoly( X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly
% 19.99/20.36 ( X ), T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP(
% 19.99/20.36 c_Polynomial_Opoly( X, T ), Y ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) )
% 19.99/20.36 }.
% 19.99/20.36 (81992) {G0,W25,D5,L2,V5,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 19.99/20.36 c_Polynomial_OpCons( X, U, T ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 19.99/20.36 c_Polynomial_OpCons( X, c_Groups_Oplus__class_Oplus( X, U, Z ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 19.99/20.36 (81993) {G0,W23,D6,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.36 ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 }.
% 19.99/20.36 (81994) {G0,W23,D6,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.36 ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 }.
% 19.99/20.36 (81995) {G0,W27,D6,L4,V3,M4} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.36 ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 19.99/20.36 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (81996) {G0,W22,D5,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.36 c_Polynomial_Osmult( X, T, c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ),
% 19.99/20.36 c_Polynomial_Osmult( X, T, Y ) ) }.
% 19.99/20.36 (81997) {G0,W31,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 19.99/20.36 ) ) }.
% 19.99/20.36 (81998) {G0,W24,D6,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.36 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus(
% 19.99/20.36 X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 }.
% 19.99/20.36 (81999) {G0,W24,D6,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.36 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus(
% 19.99/20.36 X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 }.
% 19.99/20.36 (82000) {G0,W28,D6,L4,V3,M4} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.36 ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 19.99/20.36 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 19.99/20.36 (82001) {G0,W20,D6,L2,V3,M2} { ! class_Rings_Olinordered__ring( X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 19.99/20.36 ) ) }.
% 19.99/20.36 (82002) {G0,W28,D6,L4,V3,M4} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.36 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ), ! Z =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 }.
% 19.99/20.36 (82003) {G0,W24,D6,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.36 ), Z = c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 19.99/20.36 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 19.99/20.36 (82004) {G0,W24,D6,L3,V3,M3} { ! class_Rings_Olinordered__ring__strict( X
% 19.99/20.36 ), Y = c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 19.99/20.36 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 19.99/20.36 (82005) {G0,W20,D6,L2,V3,M2} { ! class_Rings_Olinordered__ring( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 19.99/20.36 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) ) }.
% 19.99/20.36 (82006) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 19.99/20.36 Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 19.99/20.36 (82007) {G0,W18,D3,L4,V4,M4} { ! class_Groups_Oordered__comm__monoid__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 19.99/20.36 Z, Y ) ) }.
% 19.99/20.36 (82008) {G0,W18,D3,L4,V4,M4} { ! class_Groups_Oordered__comm__monoid__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 19.99/20.36 Y, Z ) ) }.
% 19.99/20.36 (82009) {G0,W23,D3,L5,V3,M5} { ! class_Groups_Oordered__comm__monoid__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 19.99/20.36 ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 }.
% 19.99/20.36 (82010) {G0,W23,D3,L5,V3,M5} { ! class_Groups_Oordered__comm__monoid__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 19.99/20.36 ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 }.
% 19.99/20.36 (82011) {G0,W27,D3,L6,V3,M6} { ! class_Groups_Oordered__comm__monoid__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 19.99/20.36 ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 19.99/20.36 = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (82012) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 19.99/20.36 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 19.99/20.36 ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 19.99/20.36 (82013) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 19.99/20.36 ( X ) ) }.
% 19.99/20.36 (82014) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 19.99/20.36 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 19.99/20.36 ) ) }.
% 19.99/20.36 (82015) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 19.99/20.36 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 19.99/20.36 ), Y ) }.
% 19.99/20.36 (82016) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 19.99/20.36 ( X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y
% 19.99/20.36 , Y ) ) }.
% 19.99/20.36 (82017) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero
% 19.99/20.36 ( X ) ), ! c_Orderings_Oord__class_Oless( X, Z,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 ) }.
% 19.99/20.36 (82018) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 19.99/20.36 ), Y ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 19.99/20.36 ( X ), Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 19.99/20.36 ( X ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 19.99/20.36 (82019) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X
% 19.99/20.36 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 19.99/20.36 }.
% 19.99/20.36 (82020) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero
% 19.99/20.36 ( X ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X
% 19.99/20.36 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 19.99/20.36 (82021) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 19.99/20.36 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 19.99/20.36 }.
% 19.99/20.36 (82022) {G0,W15,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 19.99/20.36 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 19.99/20.36 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 19.99/20.36 (82023) {G0,W18,D3,L4,V4,M4} { ! class_Rings_Olinordered__semidom( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 19.99/20.36 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 19.99/20.36 (82024) {G0,W20,D3,L4,V5,M4} { !
% 19.99/20.36 class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 19.99/20.36 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 19.99/20.36 (82025) {G0,W20,D3,L4,V5,M4} { !
% 19.99/20.36 class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 19.99/20.36 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 19.99/20.36 , Y, T ) ) }.
% 19.99/20.36 (82026) {G0,W31,D6,L5,V6,M5} { !
% 19.99/20.36 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 19.99/20.36 ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 19.99/20.36 (82027) {G0,W10,D4,L2,V2,M2} { ! class_Rings_Olinordered__semidom( X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oplus__class_Oplus( X, Y,
% 19.99/20.36 c_Groups_Oone__class_Oone( X ) ) ) }.
% 19.99/20.36 (82028) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), !
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 , c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 19.99/20.36 (82029) {G0,W11,D4,L2,V2,M2} { ! class_Groups_Oab__group__add( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 19.99/20.36 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (82030) {G0,W11,D4,L2,V2,M2} { ! class_Groups_Ogroup__add( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 19.99/20.36 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (82031) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), ! Z =
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Oplus__class_Oplus( X,
% 19.99/20.36 Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (82032) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), !
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 , Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 19.99/20.36 (82033) {G0,W11,D4,L2,V2,M2} { ! class_Groups_Ogroup__add( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Ouminus__class_Ouminus( X, Y
% 19.99/20.36 ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (82034) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), !
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 , Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 19.99/20.36 (82035) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), ! Y =
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 19.99/20.36 Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (82036) {G0,W22,D6,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), Z ), Y ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Oone__class_Oone( X ) ) ), Y
% 19.99/20.36 ) }.
% 19.99/20.36 (82037) {G0,W22,D6,L2,V3,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Z, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 19.99/20.36 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 19.99/20.36 (82038) {G0,W18,D6,L2,V2,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Y, Y ) = hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X,
% 19.99/20.36 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ), Y )
% 19.99/20.36 }.
% 19.99/20.36 (82039) {G0,W24,D5,L4,V4,M4} { ! class_Groups_Ocomm__monoid__add( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 19.99/20.36 , Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree
% 19.99/20.36 ( X, T ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.36 c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly
% 19.99/20.36 ( X ), Z, T ) ), Y ) }.
% 19.99/20.36 (82040) {G0,W21,D5,L3,V3,M3} { ! class_Groups_Ocomm__monoid__add( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 19.99/20.36 , c_Polynomial_Odegree( X, Y ) ), c_Polynomial_Odegree( X,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 19.99/20.36 c_Polynomial_Odegree( X, Y ) }.
% 19.99/20.36 (82041) {G0,W21,D5,L3,V3,M3} { ! class_Groups_Ocomm__monoid__add( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 19.99/20.36 , c_Polynomial_Odegree( X, Y ) ), c_Polynomial_Odegree( X,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) =
% 19.99/20.36 c_Polynomial_Odegree( X, Y ) }.
% 19.99/20.36 (82042) {G0,W24,D5,L4,V4,M4} { ! class_Groups_Ocomm__monoid__add( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 19.99/20.36 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 19.99/20.36 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 19.99/20.36 (82043) {G0,W19,D5,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 19.99/20.36 ( c_Polynomial_Opoly( X,
% 19.99/20.36 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 19.99/20.36 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 19.99/20.36 , Y ) ) }.
% 19.99/20.36 (82044) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X, Z
% 19.99/20.36 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 ) }.
% 19.99/20.36 (82045) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero
% 19.99/20.36 ( X ) ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 ) }.
% 19.99/20.36 (82046) {G0,W18,D3,L4,V4,M4} { ! class_Groups_Oordered__comm__monoid__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless( X
% 19.99/20.36 , T, Z ), c_Orderings_Oord__class_Oless( X, T,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 19.99/20.36 (82047) {G0,W18,D3,L4,V4,M4} { ! class_Groups_Oordered__comm__monoid__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 19.99/20.36 ), Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 19.99/20.36 ) ) }.
% 19.99/20.36 (82048) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless( X
% 19.99/20.36 , c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X
% 19.99/20.36 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 19.99/20.36 ) ) }.
% 19.99/20.36 (82049) {G0,W20,D3,L4,V3,M4} { ! class_Groups_Oordered__comm__monoid__add
% 19.99/20.36 ( X ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 19.99/20.36 ), Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 19.99/20.36 ) }.
% 19.99/20.36 (82050) {G0,W12,D4,L2,V1,M2} { ! class_Rings_Olinordered__semidom( X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 19.99/20.36 c_Groups_Oone__class_Oone( X ) ) ) }.
% 19.99/20.36 (82051) {G0,W11,D5,L1,V4,M1} { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y
% 19.99/20.36 ), X ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 19.99/20.36 (82052) {G0,W22,D6,L1,V5,M1} { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z
% 19.99/20.36 ), Y ), c_Nat_OSuc( X ) ) = hAPP( hAPP( Z, Y ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower_Opower( U, T, Z ), Y ), X ) ) }.
% 19.99/20.36 (82053) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 19.99/20.36 (82054) {G0,W16,D3,L3,V5,M3} { ! class_Orderings_Oord( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ), hAPP( Y, U ) ) }.
% 19.99/20.36 (82055) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 19.99/20.36 (82056) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 19.99/20.36 (82057) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Opreorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 19.99/20.36 (82058) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 19.99/20.36 (82059) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! Z = T,
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 19.99/20.36 (82060) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oord( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! Y = T,
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 19.99/20.36 (82061) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 19.99/20.36 (82062) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oord( X ), ! Z = Y, !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 19.99/20.36 (82063) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 19.99/20.36 (82064) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! Y = Z,
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 19.99/20.36 (82065) {G0,W16,D3,L3,V5,M3} { ! class_Orderings_Oord( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ), hAPP( Y, U ) ) }.
% 19.99/20.36 (82066) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 19.99/20.36 (82067) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), ! Z = Y,
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 19.99/20.36 (82068) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), ! Z = Y,
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 19.99/20.36 (82069) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 19.99/20.36 (82070) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 19.99/20.36 (82071) {G0,W16,D3,L3,V5,M3} { ! class_Orderings_Oord( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ), hAPP( Y, U ) ) }.
% 19.99/20.36 (82072) {G0,W22,D4,L3,V4,M3} { ! class_Orderings_Oord( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, skol8( X, Y, Z ) ), hAPP(
% 19.99/20.36 Y, skol8( X, Y, Z ) ) ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X
% 19.99/20.36 ), Z, Y ) }.
% 19.99/20.36 (82073) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y,
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 19.99/20.36 (82074) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, Y, Z ) }.
% 19.99/20.36 (82075) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, T, Z ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 19.99/20.36 (82076) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Opreorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 19.99/20.36 (82077) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Z = T,
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 19.99/20.36 (82078) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oord( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Y = T,
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 19.99/20.36 (82079) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 19.99/20.36 X, T, Z ) }.
% 19.99/20.36 (82080) {G0,W13,D2,L4,V4,M4} { ! class_Orderings_Oord( X ), ! Z = Y, !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, T ), c_Orderings_Oord__class_Oless(
% 19.99/20.36 X, Z, T ) }.
% 19.99/20.36 (82081) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, Y, Z ) }.
% 19.99/20.36 (82082) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, Y, Z ) }.
% 19.99/20.36 (82083) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Y = Z }.
% 19.99/20.36 (82084) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Z = Y }.
% 19.99/20.36 (82085) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, Y, Z ) }.
% 19.99/20.36 (82086) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, Y, Z ) }.
% 19.99/20.36 (82087) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Z = Y }.
% 19.99/20.36 (82088) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ), Z = Y,
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 19.99/20.36 X, Y, Z ) }.
% 19.99/20.36 (82089) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 19.99/20.36 X, Y, Z ), Y = Z }.
% 19.99/20.36 (82090) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Y = Z, !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 19.99/20.36 (82091) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y,
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 19.99/20.36 (82092) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 19.99/20.36 X, Y, Z ), Z = Y }.
% 19.99/20.36 (82093) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, Z ), ! c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, Z, Y ) }.
% 19.99/20.36 (82094) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 19.99/20.36 (82095) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ), Z = Y,
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 19.99/20.36 X, Y, Z ) }.
% 19.99/20.36 (82096) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Z = Y }.
% 19.99/20.36 (82097) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, Z ), ! Z = Y }.
% 19.99/20.36 (82098) {G0,W6,D2,L2,V2,M2} { ! class_Orderings_Opreorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, Y ) }.
% 19.99/20.36 (82099) {G0,W24,D6,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 19.99/20.36 ( c_Polynomial_Opoly( X, c_Polynomial_OpCons( X, T, Z ) ), Y ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( c_Polynomial_Opoly( X, Z )
% 19.99/20.36 , Y ) ) ) }.
% 19.99/20.36 (82100) {G0,W22,D4,L3,V4,M3} { ! class_Rings_Ocomm__semiring__0( X ), !
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 19.99/20.36 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.36 (82101) {G0,W27,D5,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.36 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 19.99/20.36 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 19.99/20.36 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 19.99/20.36 c_Polynomial_OpCons( X, T,
% 19.99/20.36 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) )
% 19.99/20.36 }.
% 19.99/20.36 (82102) {G0,W44,D6,L7,V6,M7} { ! class_Rings_Olinordered__semiring__1( X )
% 19.99/20.36 , ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 19.99/20.36 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 19.99/20.36 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 19.99/20.36 ), Y ) }.
% 19.99/20.36 (82103) {G0,W31,D8,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 19.99/20.36 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 19.99/20.36 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) )
% 19.99/20.36 }.
% 19.99/20.36 (82104) {G0,W31,D8,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 19.99/20.36 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 19.99/20.36 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) )
% 19.99/20.36 }.
% 19.99/20.36 (82105) {G0,W22,D4,L3,V5,M3} { ! class_Rings_Ocomm__semiring__0( X ), !
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), U,
% 19.99/20.36 c_Polynomial_Osmult( X, T, Z ) ) = c_Polynomial_OpCons( X, Y, Z ), Y =
% 19.99/20.36 hAPP( c_Polynomial_Opoly( X, U ), T ) }.
% 19.99/20.36 (82106) {G0,W21,D4,L3,V5,M3} { ! class_Rings_Ocomm__semiring__0( X ), !
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), U,
% 19.99/20.36 c_Polynomial_Osmult( X, T, Z ) ) = c_Polynomial_OpCons( X, Y, Z ), Z =
% 19.99/20.36 c_Polynomial_Osynthetic__div( X, U, T ) }.
% 19.99/20.36 (82107) {G0,W25,D5,L2,V3,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z,
% 19.99/20.36 c_Polynomial_Osmult( X, Y, c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) =
% 19.99/20.36 c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Z ), Y ),
% 19.99/20.36 c_Polynomial_Osynthetic__div( X, Z, Y ) ) }.
% 19.99/20.36 (82108) {G0,W44,D6,L7,V6,M7} { !
% 19.99/20.36 class_Rings_Olinordered__semiring__1__strict( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), U ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 19.99/20.36 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 19.99/20.36 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 19.99/20.36 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 19.99/20.36 (82109) {G0,W29,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.36 c_Polynomial_Opcompose( X, c_Polynomial_OpCons( X, T, Z ), Y ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 19.99/20.36 c_Polynomial_OpCons( X, T, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), Y ), c_Polynomial_Opcompose( X, Z, Y ) ) )
% 19.99/20.36 }.
% 19.99/20.36 (82110) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 19.99/20.36 X, T, Y ) }.
% 19.99/20.36 (82111) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Opreorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, T ), c_Orderings_Oord__class_Oless(
% 19.99/20.36 X, Z, T ) }.
% 19.99/20.36 (82112) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 19.99/20.36 (82113) {G0,W14,D2,L4,V4,M4} { ! class_Orderings_Opreorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 19.99/20.36 (82114) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Y = Z,
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 19.99/20.36 (82115) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y,
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 19.99/20.36 (82116) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 19.99/20.36 (82117) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 19.99/20.36 (82118) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), ! Z = Y, !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 19.99/20.36 (82119) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 19.99/20.36 (82120) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 19.99/20.36 (82121) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), Z = Y, !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 19.99/20.36 (82122) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), Z = Y, !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 19.99/20.36 (82123) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 19.99/20.36 (82124) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Olinorder( X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Z = Y,
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 19.99/20.36 (82125) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 19.99/20.36 (82126) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 19.99/20.36 (82127) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 19.99/20.36 (82128) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 19.99/20.36 (82129) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), ! Z = Y,
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 19.99/20.36 (82130) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 19.99/20.36 (82131) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Opreorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 19.99/20.36 (82132) {G0,W14,D2,L4,V3,M4} { ! class_Orderings_Opreorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 19.99/20.36 (82133) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 19.99/20.36 (82134) {G0,W9,D2,L3,V3,M3} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), ! Z = Y }.
% 19.99/20.36 (82135) {G0,W13,D2,L4,V3,M4} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y,
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 19.99/20.36 (82136) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 19.99/20.36 (82137) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 19.99/20.36 (82138) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 19.99/20.36 (82139) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 19.99/20.36 (82140) {G0,W10,D2,L3,V3,M3} { ! class_Orderings_Olinorder( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 19.99/20.36 (82141) {G0,W20,D6,L4,V6,M4} { ! class_Rings_Odvd( X ), !
% 19.99/20.36 class_Rings_Osemiring__0( X ), ! hBOOL( hAPP( Z, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL( hAPP( Z, skol9(
% 19.99/20.36 U, W, Z ) ) ) }.
% 19.99/20.36 (82142) {G0,W27,D6,L4,V4,M4} { ! class_Rings_Odvd( X ), !
% 19.99/20.36 class_Rings_Osemiring__0( X ), ! hBOOL( hAPP( Z, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Oplus__class_Oplus( X, skol9
% 19.99/20.36 ( X, Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) ) }.
% 19.99/20.36 (82143) {G0,W31,D6,L5,V4,M5} { ! class_Rings_Odvd( X ), !
% 19.99/20.36 class_Rings_Osemiring__0( X ), ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Oplus__class_Oplus( X, T,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 19.99/20.36 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol21( X,
% 19.99/20.36 Y, Z ) ) ) ) }.
% 19.99/20.36 (82144) {G0,W15,D3,L3,V2,M3} { ! class_Rings_Olinordered__idom( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 19.99/20.36 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 19.99/20.36 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 19.99/20.36 (82145) {G0,W15,D3,L3,V2,M3} { ! class_Rings_Olinordered__idom( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 19.99/20.36 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 19.99/20.36 (82146) {G0,W23,D7,L1,V3,M1} { hAPP( hAPP( c_Power_Opower__class_Opower(
% 19.99/20.36 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z
% 19.99/20.36 ), Y ) ), X ) = hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 19.99/20.36 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 19.99/20.36 ) }.
% 19.99/20.36 (82147) {G0,W21,D7,L3,V5,M3} { ! class_Fields_Ofield( X ), !
% 19.99/20.36 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ), U =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 19.99/20.36 }.
% 19.99/20.36 (82148) {G0,W13,D2,L3,V5,M3} { ! class_Fields_Ofield( X ), !
% 19.99/20.36 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ), alpha21( X, Y, Z, T ) }.
% 19.99/20.36 (82149) {G0,W26,D7,L4,V5,M4} { ! class_Fields_Ofield( X ), ! U =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 19.99/20.36 , ! alpha21( X, Y, Z, T ), c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 19.99/20.36 }.
% 19.99/20.36 (82150) {G0,W9,D2,L2,V4,M2} { ! alpha21( X, Y, Z, T ), alpha9( X, Z, T )
% 19.99/20.36 }.
% 19.99/20.36 (82151) {G0,W9,D2,L2,V4,M2} { ! alpha21( X, Y, Z, T ), alpha18( X, Y, T )
% 19.99/20.36 }.
% 19.99/20.36 (82152) {G0,W13,D2,L3,V4,M3} { ! alpha9( X, Z, T ), ! alpha18( X, Y, T ),
% 19.99/20.36 alpha21( X, Y, Z, T ) }.
% 19.99/20.36 (82153) {G0,W13,D4,L3,V3,M3} { ! alpha18( X, Y, Z ), Z =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha22( X, Y, Z
% 19.99/20.36 ) }.
% 19.99/20.36 (82154) {G0,W9,D4,L2,V3,M2} { ! Z = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), alpha18( X, Y, Z ) }.
% 19.99/20.36 (82155) {G0,W8,D2,L2,V3,M2} { ! alpha22( X, Y, Z ), alpha18( X, Y, Z ) }.
% 19.99/20.36 (82156) {G0,W17,D4,L3,V3,M3} { ! alpha22( X, Y, Z ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y )
% 19.99/20.36 , c_Polynomial_Odegree( X, Z ) ) }.
% 19.99/20.36 (82157) {G0,W9,D4,L2,V3,M2} { ! Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), alpha22( X, Y, Z ) }.
% 19.99/20.36 (82158) {G0,W12,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) )
% 19.99/20.36 , alpha22( X, Y, Z ) }.
% 19.99/20.36 (82159) {G0,W14,D4,L3,V3,M3} { ! alpha9( X, Y, Z ), ! Z =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.36 (82160) {G0,W9,D4,L2,V3,M2} { Z = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), alpha9( X, Y, Z ) }.
% 19.99/20.36 (82161) {G0,W9,D4,L2,V3,M2} { ! Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), alpha9( X, Y, Z ) }.
% 19.99/20.36 (82162) {G0,W35,D8,L3,V5,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.36 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ) ), hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), c_Groups_Oplus__class_Oplus
% 19.99/20.36 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ) ) }.
% 19.99/20.36 (82163) {G0,W35,D8,L3,V5,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.36 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 19.99/20.36 , Z ), X ) ), T ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 19.99/20.36 tc_Int_Oint ), Y ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ) )
% 19.99/20.36 }.
% 19.99/20.36 (82164) {G0,W22,D7,L2,V3,M2} { ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), c_Groups_Oplus__class_Oplus
% 19.99/20.36 ( tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint
% 19.99/20.36 ), Z ), X ) ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 19.99/20.36 tc_Int_Oint ), Z ), Y ) ) }.
% 19.99/20.36 (82165) {G0,W22,D7,L2,V3,M2} { ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), c_Groups_Oplus__class_Oplus
% 19.99/20.36 ( tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint
% 19.99/20.36 ), Z ), X ) ) ) ) }.
% 19.99/20.36 (82166) {G0,W26,D7,L1,V3,M1} { hAPP( hAPP( c_Power_Opower__class_Opower(
% 19.99/20.36 tc_Int_Oint ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 19.99/20.36 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 19.99/20.36 (82167) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.36 tc_Nat_Onat ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 19.99/20.36 (82168) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.36 tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.36 (82169) {G0,W30,D7,L1,V4,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 19.99/20.36 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 19.99/20.36 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 19.99/20.36 (82170) {G0,W7,D4,L1,V1,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) = X }.
% 19.99/20.36 (82171) {G0,W7,D4,L1,V1,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X
% 19.99/20.36 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 19.99/20.36 (82172) {G0,W11,D3,L2,V2,M2} { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 19.99/20.36 , Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.36 (82173) {G0,W11,D3,L2,V2,M2} { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 19.99/20.36 , Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.36 (82174) {G0,W15,D3,L3,V2,M3} { ! Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Nat_Onat ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.36 (82175) {G0,W10,D3,L2,V2,M2} { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 19.99/20.36 , Y, X ) = Y, X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.36 (82176) {G0,W11,D4,L1,V2,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 19.99/20.36 , c_Nat_OSuc( X ) ) = c_Nat_OSuc( c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Nat_Onat, Y, X ) ) }.
% 19.99/20.36 (82177) {G0,W11,D4,L1,V2,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 19.99/20.36 c_Nat_OSuc( Y ), X ) = c_Nat_OSuc( c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Nat_Onat, Y, X ) ) }.
% 19.99/20.36 (82178) {G0,W11,D4,L1,V2,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 19.99/20.36 c_Nat_OSuc( Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 19.99/20.36 c_Nat_OSuc( X ) ) }.
% 19.99/20.36 (82179) {G0,W7,D3,L1,V2,M1} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.36 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), Y ) }.
% 19.99/20.36 (82180) {G0,W7,D3,L1,V2,M1} { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.36 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), X ) }.
% 19.99/20.36 (82181) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 19.99/20.36 (82182) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 19.99/20.36 (82183) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 19.99/20.36 (82184) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 19.99/20.36 (82185) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 19.99/20.36 (82186) {G0,W18,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z )
% 19.99/20.36 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 19.99/20.36 ( tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) )
% 19.99/20.36 }.
% 19.99/20.36 (82187) {G0,W17,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, Y, X ), ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 19.99/20.36 (82188) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 19.99/20.36 (82189) {G0,W17,D5,L2,V2,M2} { ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), c_Groups_Oplus__class_Oplus
% 19.99/20.36 ( tc_Nat_Onat, X, Y ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 19.99/20.36 tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.36 (82190) {G0,W17,D5,L2,V2,M2} { ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), c_Groups_Oplus__class_Oplus
% 19.99/20.36 ( tc_Nat_Onat, X, Y ) ) ) }.
% 19.99/20.36 (82191) {G0,W7,D3,L1,V2,M1} { c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 19.99/20.36 (82192) {G0,W7,D3,L1,V2,M1} { c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 19.99/20.36 (82193) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Nat_Onat, Y, X ), X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 19.99/20.36 skol10( X, Y ) ) }.
% 19.99/20.36 (82194) {G0,W10,D3,L2,V3,M2} { ! X = c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Nat_Onat, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 19.99/20.36 ) }.
% 19.99/20.36 (82195) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 19.99/20.36 (82196) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 19.99/20.36 (82197) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 19.99/20.36 (82198) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 19.99/20.36 (82199) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 19.99/20.36 (82200) {G0,W18,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T
% 19.99/20.36 , Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 19.99/20.36 (82201) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 19.99/20.36 (82202) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 19.99/20.36 (82203) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 19.99/20.36 (82204) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 19.99/20.36 (82205) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 19.99/20.36 (82206) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 19.99/20.36 (82207) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 19.99/20.36 (82208) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 19.99/20.36 (82209) {G0,W14,D3,L3,V4,M3} { ! class_Orderings_Oord( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 19.99/20.36 (82210) {G0,W14,D3,L3,V4,M3} { ! class_Orderings_Oord( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z ) }.
% 19.99/20.36 (82211) {G0,W20,D3,L4,V4,M4} { ! class_Orderings_Oord( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 19.99/20.36 (82212) {G0,W17,D2,L4,V7,M4} { ! class_Fields_Ofield( X ), !
% 19.99/20.36 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ), ! c_Polynomial_Opdivmod__rel
% 19.99/20.36 ( X, U, T, V0, W ), Z = V0 }.
% 19.99/20.36 (82213) {G0,W17,D2,L4,V7,M4} { ! class_Fields_Ofield( X ), !
% 19.99/20.36 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ), ! c_Polynomial_Opdivmod__rel
% 19.99/20.36 ( X, U, T, V0, W ), Y = W }.
% 19.99/20.36 (82214) {G0,W17,D2,L4,V7,M4} { ! class_Fields_Ofield( X ), !
% 19.99/20.36 c_Polynomial_Opdivmod__rel( X, T, Z, U, Y ), ! c_Polynomial_Opdivmod__rel
% 19.99/20.36 ( X, T, Z, V0, W ), Y = W }.
% 19.99/20.36 (82215) {G0,W17,D2,L4,V7,M4} { ! class_Fields_Ofield( X ), !
% 19.99/20.36 c_Polynomial_Opdivmod__rel( X, T, Z, Y, U ), ! c_Polynomial_Opdivmod__rel
% 19.99/20.36 ( X, T, Z, W, V0 ), Y = W }.
% 19.99/20.36 (82216) {G0,W12,D4,L2,V2,M2} { ! class_Fields_Ofield( X ),
% 19.99/20.36 c_Polynomial_Opdivmod__rel( X, Y, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), Y ) }.
% 19.99/20.36 (82217) {G0,W14,D4,L2,V2,M2} { ! class_Fields_Ofield( X ),
% 19.99/20.36 c_Polynomial_Opdivmod__rel( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), Y, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ) ) }.
% 19.99/20.36 (82218) {G0,W15,D4,L3,V4,M3} { ! class_Fields_Ofield( X ), !
% 19.99/20.36 c_Polynomial_Opdivmod__rel( X, T, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), Z, Y ), Z = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.36 (82219) {G0,W13,D4,L3,V4,M3} { ! class_Fields_Ofield( X ), !
% 19.99/20.36 c_Polynomial_Opdivmod__rel( X, T, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }.
% 19.99/20.36 (82220) {G0,W18,D4,L4,V4,M4} { ! class_Fields_Ofield( X ), ! Z =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Y = T,
% 19.99/20.36 c_Polynomial_Opdivmod__rel( X, T, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 19.99/20.36 (82221) {G0,W15,D4,L3,V4,M3} { ! class_Fields_Ofield( X ), !
% 19.99/20.36 c_Polynomial_Opdivmod__rel( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.36 (82222) {G0,W15,D4,L3,V4,M3} { ! class_Fields_Ofield( X ), !
% 19.99/20.36 c_Polynomial_Opdivmod__rel( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.36 (82223) {G0,W20,D4,L4,V4,M4} { ! class_Fields_Ofield( X ), ! Z =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 19.99/20.36 c_Polynomial_Opdivmod__rel( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 19.99/20.36 (82224) {G0,W23,D3,L3,V6,M3} { ! class_Fields_Ofield( X ), !
% 19.99/20.36 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ), c_Polynomial_Opdivmod__rel(
% 19.99/20.36 X, c_Polynomial_Osmult( X, W, U ), T, c_Polynomial_Osmult( X, W, Z ),
% 19.99/20.36 c_Polynomial_Osmult( X, W, Y ) ) }.
% 19.99/20.36 (82225) {G0,W28,D7,L2,V4,M2} { ! class_Rings_Ocomm__semiring__1( X ), hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Nat_Onat, Z, Y ) ) }.
% 19.99/20.36 (82226) {G0,W28,D7,L2,V4,M2} { ! class_Groups_Omonoid__mult( X ), hAPP(
% 19.99/20.36 hAPP( c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus
% 19.99/20.36 ( tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 19.99/20.36 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 19.99/20.36 (82227) {G0,W14,D4,L3,V2,M3} { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Nat_Onat ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ),
% 19.99/20.36 alpha10( X, Y ), alpha19( X, Y ) }.
% 19.99/20.36 (82228) {G0,W11,D4,L2,V2,M2} { ! alpha10( X, Y ), c_Nat_OSuc(
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 19.99/20.36 (82229) {G0,W11,D4,L2,V2,M2} { ! alpha19( X, Y ), c_Nat_OSuc(
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 19.99/20.36 (82230) {G0,W7,D3,L2,V2,M2} { ! alpha19( X, Y ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.36 (82231) {G0,W8,D4,L2,V2,M2} { ! alpha19( X, Y ), X = c_Nat_OSuc(
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 19.99/20.36 (82232) {G0,W12,D4,L3,V2,M3} { ! Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Nat_Onat ), ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 19.99/20.36 ) ), alpha19( X, Y ) }.
% 19.99/20.36 (82233) {G0,W8,D4,L2,V2,M2} { ! alpha10( X, Y ), Y = c_Nat_OSuc(
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 19.99/20.36 (82234) {G0,W7,D3,L2,V2,M2} { ! alpha10( X, Y ), X =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.36 (82235) {G0,W12,D4,L3,V2,M3} { ! Y = c_Nat_OSuc(
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha10( X, Y ) }.
% 19.99/20.36 (82236) {G0,W14,D4,L3,V2,M3} { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 19.99/20.36 , Y, X ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 19.99/20.36 alpha11( X, Y ), alpha20( X, Y ) }.
% 19.99/20.36 (82237) {G0,W11,D4,L2,V2,M2} { ! alpha11( X, Y ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 19.99/20.36 (82238) {G0,W11,D4,L2,V2,M2} { ! alpha20( X, Y ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 19.99/20.36 (82239) {G0,W7,D3,L2,V2,M2} { ! alpha20( X, Y ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.36 (82240) {G0,W8,D4,L2,V2,M2} { ! alpha20( X, Y ), X = c_Nat_OSuc(
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 19.99/20.36 (82241) {G0,W12,D4,L3,V2,M3} { ! Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Nat_Onat ), ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 19.99/20.36 ) ), alpha20( X, Y ) }.
% 19.99/20.36 (82242) {G0,W8,D4,L2,V2,M2} { ! alpha11( X, Y ), Y = c_Nat_OSuc(
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 19.99/20.36 (82243) {G0,W7,D3,L2,V2,M2} { ! alpha11( X, Y ), X =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.36 (82244) {G0,W12,D4,L3,V2,M3} { ! Y = c_Nat_OSuc(
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha11( X, Y ) }.
% 19.99/20.36 (82245) {G0,W18,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 19.99/20.36 (82246) {G0,W13,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 19.99/20.36 (82247) {G0,W13,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 19.99/20.36 (82248) {G0,W8,D4,L1,V2,M1} { c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.36 Y, c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 19.99/20.36 (82249) {G0,W8,D4,L1,V2,M1} { c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.36 Y, c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 19.99/20.36 (82250) {G0,W13,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, Y, X ), X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Nat_Onat, Y, skol11( X, Y ) ) ) }.
% 19.99/20.36 (82251) {G0,W11,D4,L2,V3,M2} { ! X = c_Nat_OSuc(
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 19.99/20.36 (82252) {G0,W17,D6,L1,V2,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.36 tc_Nat_Onat ), c_Nat_OSuc( Y ) ), X ) = c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Nat_Onat, X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 19.99/20.36 , Y ), X ) ) }.
% 19.99/20.36 (82253) {G0,W17,D6,L1,V2,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.36 tc_Nat_Onat ), Y ), c_Nat_OSuc( X ) ) = c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Nat_Onat, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 19.99/20.36 , Y ), X ) ) }.
% 19.99/20.36 (82254) {G0,W8,D4,L1,V1,M1} { c_Nat_OSuc( X ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 19.99/20.36 tc_Nat_Onat ), X ) }.
% 19.99/20.36 (82255) {G0,W8,D4,L1,V1,M1} { c_Nat_OSuc( X ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 19.99/20.36 tc_Nat_Onat ) ) }.
% 19.99/20.36 (82256) {G0,W36,D7,L4,V8,M4} { ! class_Fields_Ofield( X ), !
% 19.99/20.36 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ), ! c_Polynomial_Opdivmod__rel
% 19.99/20.36 ( X, Z, V1, V0, W ), c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 19.99/20.36 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 19.99/20.36 ) }.
% 19.99/20.36 (82257) {G0,W21,D7,L2,V3,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 19.99/20.36 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z
% 19.99/20.36 ), Y ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree
% 19.99/20.36 ( X, Z ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 19.99/20.36 (82258) {G0,W30,D7,L4,V3,M4} { ! class_Rings_Oidom( X ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 19.99/20.36 c_Polynomial_Odegree( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), Y ), Z ) ) = c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Nat_Onat, c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) )
% 19.99/20.36 }.
% 19.99/20.36 (82259) {G0,W28,D6,L2,V5,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 19.99/20.36 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 19.99/20.36 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 19.99/20.36 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 19.99/20.36 (82260) {G0,W27,D5,L5,V2,M5} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.36 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ), X = Y }.
% 19.99/20.36 (82261) {G0,W16,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 19.99/20.36 (82262) {G0,W16,D5,L3,V2,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 19.99/20.36 ) }.
% 19.99/20.36 (82263) {G0,W16,D5,L2,V2,M2} { ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), c_Groups_Ouminus__class_Ouminus
% 19.99/20.36 ( tc_Int_Oint, Y ) ), X ) ) }.
% 19.99/20.36 (82264) {G0,W16,D5,L2,V2,M2} { ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), c_Groups_Ouminus__class_Ouminus
% 19.99/20.36 ( tc_Int_Oint, Y ) ), X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 19.99/20.36 ( tc_Int_Oint ), Y ), X ) ) }.
% 19.99/20.36 (82265) {G0,W16,D5,L2,V2,M2} { ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ), hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ) }.
% 19.99/20.36 (82266) {G0,W16,D5,L2,V2,M2} { ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ), hBOOL( hAPP( hAPP
% 19.99/20.36 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 19.99/20.36 (82267) {G0,W28,D7,L3,V3,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), Z =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 19.99/20.36 (82268) {G0,W28,D7,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Int_Oint ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint
% 19.99/20.36 ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint
% 19.99/20.36 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) )
% 19.99/20.36 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) )
% 19.99/20.36 }.
% 19.99/20.36 (82269) {G0,W28,D7,L3,V3,M3} { X = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Int_Oint ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint
% 19.99/20.36 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) )
% 19.99/20.36 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) )
% 19.99/20.36 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) )
% 19.99/20.36 }.
% 19.99/20.36 (82270) {G0,W39,D8,L2,V3,M2} { ! class_Rings_Ocomm__semiring__0( X ), hAPP
% 19.99/20.36 ( c_Polynomial_Ocoeff( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), Z ), Y ) ), c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 19.99/20.36 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 19.99/20.36 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) ), hAPP(
% 19.99/20.36 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 19.99/20.36 (82271) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 19.99/20.36 ( X ), ! c_Groups_Oplus__class_Oplus( X, Y, Y ) =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 }.
% 19.99/20.36 (82272) {G0,W13,D3,L3,V2,M3} { ! class_Groups_Olinordered__ab__group__add
% 19.99/20.36 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 }.
% 19.99/20.36 (82273) {G0,W16,D4,L3,V2,M3} { ! class_Rings_Olinordered__idom( X ), !
% 19.99/20.36 c_Polynomial_Opos__poly( X, Y ), c_Orderings_Oord__class_Oless( X,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 19.99/20.36 c_Polynomial_Odegree( X, Y ) ) ) }.
% 19.99/20.36 (82274) {G0,W16,D4,L3,V2,M3} { ! class_Rings_Olinordered__idom( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 19.99/20.36 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ),
% 19.99/20.36 c_Polynomial_Opos__poly( X, Y ) }.
% 19.99/20.36 (82275) {G0,W15,D3,L4,V3,M4} { ! class_Rings_Olinordered__idom( X ), !
% 19.99/20.36 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ),
% 19.99/20.36 c_Polynomial_Opos__poly( X, Y ), alpha12( X, Y, Z ) }.
% 19.99/20.36 (82276) {G0,W11,D3,L3,V3,M3} { ! class_Rings_Olinordered__idom( X ), !
% 19.99/20.36 c_Polynomial_Opos__poly( X, Y ), c_Polynomial_Opos__poly( X,
% 19.99/20.36 c_Polynomial_OpCons( X, Z, Y ) ) }.
% 19.99/20.36 (82277) {G0,W12,D3,L3,V3,M3} { ! class_Rings_Olinordered__idom( X ), !
% 19.99/20.36 alpha12( X, Y, Z ), c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z
% 19.99/20.36 , Y ) ) }.
% 19.99/20.36 (82278) {G0,W9,D4,L2,V3,M2} { ! alpha12( X, Y, Z ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.36 (82279) {G0,W9,D3,L2,V3,M2} { ! alpha12( X, Y, Z ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 19.99/20.36 }.
% 19.99/20.36 (82280) {G0,W14,D4,L3,V3,M3} { ! Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), Z ), alpha12( X, Y, Z ) }.
% 19.99/20.36 (82281) {G0,W19,D6,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra(
% 19.99/20.36 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 19.99/20.36 (82282) {G0,W11,D5,L1,V1,M1} { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 19.99/20.36 , c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 19.99/20.36 tc_Int_Oint ), X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 19.99/20.36 (82283) {G0,W17,D5,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 19.99/20.36 tc_Int_Oint ), X ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 19.99/20.36 (82284) {G0,W17,D5,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Int_Oint, X, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 19.99/20.36 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 19.99/20.36 (82285) {G0,W14,D4,L2,V1,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 19.99/20.36 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 19.99/20.36 (82286) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, X,
% 19.99/20.36 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 19.99/20.36 (82287) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 19.99/20.36 tc_Int_Oint ) ) ) }.
% 19.99/20.36 (82288) {G0,W15,D4,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, X,
% 19.99/20.36 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X }.
% 19.99/20.36 (82289) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 19.99/20.36 tc_Int_Oint ) ) ) }.
% 19.99/20.36 (82290) {G0,W11,D4,L2,V2,M2} { ! Y = X, c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, X,
% 19.99/20.36 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 19.99/20.36 (82291) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.36 tc_Int_Oint ), Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 19.99/20.36 (82292) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 19.99/20.36 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 19.99/20.36 (82293) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 19.99/20.36 tc_Int_Oint ) ), X ) }.
% 19.99/20.36 (82294) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.36 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 19.99/20.36 (82295) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 19.99/20.36 tc_Int_Oint ) ), X ) }.
% 19.99/20.36 (82296) {G0,W15,D4,L1,V3,M1} { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ), X ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 19.99/20.36 ( tc_Int_Oint, Y, X ) ) }.
% 19.99/20.36 (82297) {G0,W15,D4,L1,V3,M1} { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z
% 19.99/20.36 , c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus
% 19.99/20.36 ( tc_Int_Oint, Z, X ) ) }.
% 19.99/20.36 (82298) {G0,W9,D3,L1,V2,M1} { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y
% 19.99/20.36 , X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 19.99/20.36 (82299) {G0,W7,D4,L1,V1,M1} { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X
% 19.99/20.36 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) = X }.
% 19.99/20.36 (82300) {G0,W7,D4,L1,V1,M1} { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ) = X }.
% 19.99/20.36 (82301) {G0,W9,D3,L1,V2,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 19.99/20.36 , X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 19.99/20.36 (82302) {G0,W15,D4,L1,V3,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z
% 19.99/20.36 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus
% 19.99/20.36 ( tc_Nat_Onat, Z, X ) ) }.
% 19.99/20.36 (82303) {G0,W15,D4,L1,V3,M1} { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 19.99/20.36 ( tc_Nat_Onat, Y, X ) ) }.
% 19.99/20.36 (82304) {G0,W12,D3,L2,V3,M2} { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 19.99/20.36 , Z, Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 19.99/20.36 (82305) {G0,W12,D3,L2,V3,M2} { ! Y = X, c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Nat_Onat, Z, Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X )
% 19.99/20.36 }.
% 19.99/20.36 (82306) {G0,W12,D3,L2,V3,M2} { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 19.99/20.36 , Z, Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 19.99/20.36 (82307) {G0,W12,D3,L2,V3,M2} { ! Z = X, c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Nat_Onat, Z, Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y )
% 19.99/20.36 }.
% 19.99/20.36 (82308) {G0,W18,D3,L3,V4,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Int_Oint, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T
% 19.99/20.36 , Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, T ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }.
% 19.99/20.36 (82309) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 19.99/20.36 (82310) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, Z ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }.
% 19.99/20.36 (82311) {G0,W15,D4,L1,V2,M1} { c_Groups_Ouminus__class_Ouminus(
% 19.99/20.36 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 19.99/20.36 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) )
% 19.99/20.36 }.
% 19.99/20.36 (82312) {G0,W9,D4,L1,V1,M1} { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ), X ) =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 19.99/20.36 (82313) {G0,W7,D4,L1,V0,M1} { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint
% 19.99/20.36 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 19.99/20.36 (82314) {G0,W4,D2,L1,V1,M1} { c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Int_Oint, X, X ) }.
% 19.99/20.36 (82315) {G0,W7,D4,L1,V1,M1} { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint
% 19.99/20.36 , c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 19.99/20.36 (82316) {G0,W8,D2,L2,V2,M2} { c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Int_Oint, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y
% 19.99/20.36 ) }.
% 19.99/20.36 (82317) {G0,W8,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Int_Oint
% 19.99/20.36 , Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 19.99/20.36 (82318) {G0,W7,D2,L2,V2,M2} { ! c_Orderings_Oord__class_Oless( tc_Int_Oint
% 19.99/20.36 , Y, X ), ! Y = X }.
% 19.99/20.36 (82319) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Int_Oint, Y, X ), Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y
% 19.99/20.36 , X ) }.
% 19.99/20.36 (82320) {G0,W11,D2,L3,V2,M3} { c_Orderings_Oord__class_Oless( tc_Int_Oint
% 19.99/20.36 , Y, X ), Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 19.99/20.36 (82321) {G0,W12,D2,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Int_Oint, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 19.99/20.36 , Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 19.99/20.36 (82322) {G0,W11,D2,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Int_Oint, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 19.99/20.36 , Y ), Y = X }.
% 19.99/20.36 (82323) {G0,W23,D7,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.36 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 19.99/20.36 Z ), Y ) ), X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint
% 19.99/20.36 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X
% 19.99/20.36 ) ) }.
% 19.99/20.36 (82324) {G0,W17,D6,L1,V2,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.36 tc_Int_Oint ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 19.99/20.36 (82325) {G0,W13,D5,L1,V2,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.36 tc_Int_Oint ), Y ), X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.36 tc_Int_Oint ), X ), Y ) }.
% 19.99/20.36 (82326) {G0,W9,D5,L1,V1,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.36 tc_Int_Oint ), X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 19.99/20.36 (82327) {G0,W9,D5,L1,V1,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.36 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 19.99/20.36 (82328) {G0,W23,D5,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Int_Oint, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 19.99/20.36 (82329) {G0,W18,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! hAPP(
% 19.99/20.36 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 19.99/20.36 c_Groups_Oone__class_Oone( tc_Int_Oint ), X = c_Groups_Oone__class_Oone(
% 19.99/20.36 tc_Int_Oint ) }.
% 19.99/20.36 (82330) {G0,W18,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! hAPP(
% 19.99/20.36 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 19.99/20.36 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y = c_Groups_Oone__class_Oone(
% 19.99/20.36 tc_Int_Oint ) }.
% 19.99/20.36 (82331) {G0,W22,D5,L4,V2,M4} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! X =
% 19.99/20.36 c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y = c_Groups_Oone__class_Oone
% 19.99/20.36 ( tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 19.99/20.36 , X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 19.99/20.36 (82332) {G0,W10,D3,L2,V1,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Int_Oint ), X ) }.
% 19.99/20.36 (82333) {G0,W10,D3,L2,V1,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 19.99/20.36 ( tc_Int_Oint ), X ) }.
% 19.99/20.36 (82334) {G0,W6,D3,L1,V0,M1} { c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 19.99/20.36 tc_Int_Oint ) ) }.
% 19.99/20.36 (82335) {G0,W5,D3,L1,V0,M1} { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 19.99/20.36 = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 19.99/20.36 (82336) {G0,W7,D4,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ), !
% 19.99/20.36 c_Polynomial_Opos__poly( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ) ) }.
% 19.99/20.36 (82337) {G0,W17,D6,L4,V3,M4} { ! class_Rings_Olinordered__idom( X ), !
% 19.99/20.36 c_Polynomial_Opos__poly( X, Y ), ! c_Polynomial_Opos__poly( X, Z ),
% 19.99/20.36 c_Polynomial_Opos__poly( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }.
% 19.99/20.36 (82338) {G0,W15,D4,L4,V3,M4} { ! class_Rings_Olinordered__idom( X ), !
% 19.99/20.36 c_Polynomial_Opos__poly( X, Y ), ! c_Polynomial_Opos__poly( X, Z ),
% 19.99/20.36 c_Polynomial_Opos__poly( X, c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 19.99/20.36 (82339) {G0,W16,D4,L4,V2,M4} { ! class_Rings_Olinordered__idom( X ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 19.99/20.36 c_Polynomial_Opos__poly( X, Y ), c_Polynomial_Opos__poly( X,
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 19.99/20.36 (82340) {G0,W12,D5,L2,V2,M2} { ! class_RealVector_Oreal__normed__algebra(
% 19.99/20.36 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) ), Y ) = c_Groups_Ozero__class_Ozero( X
% 19.99/20.36 ) }.
% 19.99/20.36 (82341) {G0,W12,D5,L2,V2,M2} { ! class_RealVector_Oreal__normed__algebra(
% 19.99/20.36 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) ), Y ) = c_Groups_Ozero__class_Ozero( X
% 19.99/20.36 ) }.
% 19.99/20.36 (82342) {G0,W12,D5,L2,V2,M2} { ! class_RealVector_Oreal__normed__algebra(
% 19.99/20.36 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (82343) {G0,W12,D5,L2,V2,M2} { ! class_RealVector_Oreal__normed__algebra(
% 19.99/20.36 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (82344) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 19.99/20.36 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, T, Z ) ), Y ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), T ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y )
% 19.99/20.36 ) }.
% 19.99/20.36 (82345) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 19.99/20.36 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, T, Z ) ), Y ) =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), T ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y )
% 19.99/20.36 ) }.
% 19.99/20.36 (82346) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 19.99/20.36 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 19.99/20.36 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 19.99/20.36 (82347) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 19.99/20.36 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 19.99/20.36 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 19.99/20.36 (82348) {G0,W19,D6,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra(
% 19.99/20.36 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) =
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 19.99/20.36 (82349) {G0,W19,D6,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra(
% 19.99/20.36 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) =
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 19.99/20.36 (82350) {G0,W19,D6,L2,V3,M2} { ! class_RealVector_Oreal__normed__algebra(
% 19.99/20.36 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 19.99/20.36 (82351) {G0,W26,D6,L4,V3,M4} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! X =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 19.99/20.36 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 19.99/20.36 (82352) {G0,W25,D6,L4,V3,M4} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! X =
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 19.99/20.36 ( tc_Int_Oint ), Y ) }.
% 19.99/20.36 (82353) {G0,W27,D6,L4,V3,M4} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 19.99/20.36 (82354) {G0,W54,D6,L7,V6,M7} { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 19.99/20.36 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T )
% 19.99/20.36 = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 19.99/20.36 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 19.99/20.36 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 19.99/20.36 (82355) {G0,W37,D6,L5,V5,M5} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 19.99/20.36 (82356) {G0,W54,D6,L7,V6,M7} { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 19.99/20.36 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T )
% 19.99/20.36 = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 19.99/20.36 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 19.99/20.36 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 19.99/20.36 (82357) {G0,W37,D6,L5,V5,M5} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 19.99/20.36 (82358) {G0,W28,D6,L4,V3,M4} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ),
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 19.99/20.36 (82359) {G0,W15,D5,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 19.99/20.36 (82360) {G0,W20,D5,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 19.99/20.36 (82361) {G0,W6,D3,L1,V0,M1} { c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 19.99/20.36 (82362) {G0,W6,D3,L1,V0,M1} { c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 19.99/20.36 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 19.99/20.36 (82363) {G0,W18,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Int_Oint, X, Y ) ) }.
% 19.99/20.36 (82364) {G0,W12,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Nat_Onat, Y, X ), X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 19.99/20.36 skol12( X, Y ) ) }.
% 19.99/20.36 (82365) {G0,W10,D3,L2,V3,M2} { ! X = c_Groups_Oplus__class_Oplus(
% 19.99/20.36 tc_Nat_Onat, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 19.99/20.36 ) }.
% 19.99/20.36 (82366) {G0,W14,D3,L3,V3,M3} { ! class_Lattices_Oboolean__algebra( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 19.99/20.36 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 19.99/20.36 (82367) {G0,W10,D5,L2,V2,M2} { ! class_Lattices_Oab__semigroup__idem__mult
% 19.99/20.36 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 19.99/20.36 (82368) {G0,W10,D5,L2,V2,M2} { ! class_Lattices_Oab__semigroup__idem__mult
% 19.99/20.36 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 19.99/20.36 (82369) {G0,W20,D6,L2,V3,M2} { ! class_Lattices_Oab__semigroup__idem__mult
% 19.99/20.36 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 19.99/20.36 (82370) {G0,W9,D4,L2,V2,M2} { ! class_Lattices_Oboolean__algebra( X ),
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 19.99/20.36 ) ) = Y }.
% 19.99/20.36 (82371) {G0,W15,D5,L2,V4,M2} { ! class_Groups_Ouminus( X ), hAPP(
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( tc_fun( T, X ), Z ), Y ) =
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y ) ) }.
% 19.99/20.36 (82372) {G0,W12,D3,L3,V3,M3} { ! class_Lattices_Oboolean__algebra( X ), !
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 19.99/20.36 ( X, Y ), Z = Y }.
% 19.99/20.36 (82373) {G0,W12,D3,L3,V3,M3} { ! class_Lattices_Oboolean__algebra( X ), !
% 19.99/20.36 Z = Y, c_Groups_Ouminus__class_Ouminus( X, Z ) =
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 19.99/20.36 (82374) {G0,W14,D3,L3,V3,M3} { ! class_Lattices_Oboolean__algebra( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 19.99/20.36 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 19.99/20.36 (82375) {G0,W14,D3,L3,V3,M3} { ! class_Lattices_Oboolean__algebra( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 19.99/20.36 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 19.99/20.36 (82376) {G0,W15,D3,L3,V5,M3} { ! class_Groups_Ozero( X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, skol13( T, U, Z ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 19.99/20.36 Y ), Z ) }.
% 19.99/20.36 (82377) {G0,W19,D4,L3,V3,M3} { ! class_Groups_Ozero( X ), ! hAPP(
% 19.99/20.36 c_Polynomial_Ocoeff( X, Y ), skol13( X, Y, Z ) ) =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 tc_Nat_Onat, c_Polynomial_Odegree( X, Y ), Z ) }.
% 19.99/20.36 (82378) {G0,W32,D7,L5,V5,M5} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), hBOOL( hAPP
% 19.99/20.36 ( Y, skol14( Z, Y ) ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint
% 19.99/20.36 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U )
% 19.99/20.36 ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP(
% 19.99/20.36 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 19.99/20.36 (82379) {G0,W35,D7,L5,V4,M5} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! hBOOL(
% 19.99/20.36 hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, skol14( X, Y ), X ) )
% 19.99/20.36 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL( hAPP( Y, T ) )
% 19.99/20.36 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, hAPP( hAPP
% 19.99/20.36 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ) }.
% 19.99/20.36 (82380) {G0,W28,D5,L4,V3,M4} { ! class_Fields_Ofield( X ), ! Z =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP(
% 19.99/20.36 c_Polynomial_Ocoeff( X, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 19.99/20.36 c_Polynomial_Odegree( X, c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (82381) {G0,W23,D5,L3,V3,M3} { ! class_Fields_Ofield( X ), Z =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP(
% 19.99/20.36 c_Polynomial_Ocoeff( X, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 19.99/20.36 c_Polynomial_Odegree( X, c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) =
% 19.99/20.36 c_Groups_Oone__class_Oone( X ) }.
% 19.99/20.36 (82382) {G0,W23,D5,L3,V3,M3} { ! class_Fields_Ofield( X ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP(
% 19.99/20.36 c_Polynomial_Ocoeff( X, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 19.99/20.36 c_Polynomial_Odegree( X, c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) =
% 19.99/20.36 c_Groups_Oone__class_Oone( X ) }.
% 19.99/20.36 (82383) {G0,W15,D4,L3,V3,M3} { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero
% 19.99/20.36 ( tc_Nat_Onat ) ) ), ! hBOOL( hAPP( X, Y ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol15( Z, Y ), Y ) }.
% 19.99/20.36 (82384) {G0,W19,D4,L4,V3,M4} { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero
% 19.99/20.36 ( tc_Nat_Onat ) ) ), ! hBOOL( hAPP( X, Y ) ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, skol15( X, Y ) ), !
% 19.99/20.36 hBOOL( hAPP( X, Z ) ) }.
% 19.99/20.36 (82385) {G0,W19,D5,L3,V2,M3} { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero
% 19.99/20.36 ( tc_Nat_Onat ) ) ), ! hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, skol15( X, Y ),
% 19.99/20.36 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 19.99/20.36 (82386) {G0,W13,D6,L2,V3,M2} { ! class_Fields_Ofield( X ), hBOOL( hAPP(
% 19.99/20.36 hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ),
% 19.99/20.36 c_Polynomial_Opoly__gcd( X, Z, Y ) ), Z ) ) }.
% 19.99/20.36 (82387) {G0,W13,D6,L2,V3,M2} { ! class_Fields_Ofield( X ), hBOOL( hAPP(
% 19.99/20.36 hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ),
% 19.99/20.36 c_Polynomial_Opoly__gcd( X, Z, Y ) ), Y ) ) }.
% 19.99/20.36 (82388) {G0,W14,D5,L2,V3,M2} { ! class_Fields_Ofield( X ),
% 19.99/20.36 c_Polynomial_Opoly__gcd( X, c_Groups_Ouminus__class_Ouminus(
% 19.99/20.36 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Polynomial_Opoly__gcd( X, Z, Y )
% 19.99/20.36 }.
% 19.99/20.36 (82389) {G0,W14,D5,L2,V3,M2} { ! class_Fields_Ofield( X ),
% 19.99/20.36 c_Polynomial_Opoly__gcd( X, Z, c_Groups_Ouminus__class_Ouminus(
% 19.99/20.36 tc_Polynomial_Opoly( X ), Y ) ) = c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 19.99/20.36 (82390) {G0,W15,D4,L3,V3,M3} { ! class_Fields_Ofield( X ), !
% 19.99/20.36 c_Polynomial_Opoly__gcd( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.36 (82391) {G0,W15,D4,L3,V3,M3} { ! class_Fields_Ofield( X ), !
% 19.99/20.36 c_Polynomial_Opoly__gcd( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.36 (82392) {G0,W20,D4,L4,V3,M4} { ! class_Fields_Ofield( X ), ! Z =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 19.99/20.36 c_Polynomial_Opoly__gcd( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.36 (82393) {G0,W14,D5,L2,V1,M2} { ! class_Fields_Ofield( X ),
% 19.99/20.36 c_Polynomial_Opoly__gcd( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.36 (82394) {G0,W17,D4,L2,V4,M2} { ! class_Fields_Ofield( X ),
% 19.99/20.36 c_Polynomial_Opoly__gcd( X, c_Polynomial_Opoly__gcd( X, T, Z ), Y ) =
% 19.99/20.36 c_Polynomial_Opoly__gcd( X, T, c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 19.99/20.36 (82395) {G0,W17,D4,L2,V4,M2} { ! class_Fields_Ofield( X ),
% 19.99/20.36 c_Polynomial_Opoly__gcd( X, T, c_Polynomial_Opoly__gcd( X, Z, Y ) ) =
% 19.99/20.36 c_Polynomial_Opoly__gcd( X, Z, c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 19.99/20.36 (82396) {G0,W11,D3,L2,V3,M2} { ! class_Fields_Ofield( X ),
% 19.99/20.36 c_Polynomial_Opoly__gcd( X, Z, Y ) = c_Polynomial_Opoly__gcd( X, Y, Z )
% 19.99/20.36 }.
% 19.99/20.36 (82397) {G0,W21,D6,L3,V4,M3} { ! class_Fields_Ofield( X ), ! hBOOL( hAPP(
% 19.99/20.36 hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 19.99/20.36 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ), hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Z ) ) }.
% 19.99/20.36 (82398) {G0,W21,D6,L3,V4,M3} { ! class_Fields_Ofield( X ), ! hBOOL( hAPP(
% 19.99/20.36 hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 19.99/20.36 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ), hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 19.99/20.36 (82399) {G0,W29,D6,L4,V4,M4} { ! class_Fields_Ofield( X ), ! hBOOL( hAPP(
% 19.99/20.36 hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Z ) ), !
% 19.99/20.36 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 19.99/20.36 , T ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Opoly__gcd( X, Z, Y ) ) )
% 19.99/20.36 }.
% 19.99/20.36 (82400) {G0,W29,D6,L4,V4,M4} { ! class_Fields_Ofield( X ), ! hBOOL( hAPP(
% 19.99/20.36 hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), !
% 19.99/20.36 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 19.99/20.36 , Z ), T ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), Z ), c_Polynomial_Opoly__gcd( X, Y, T ) ) )
% 19.99/20.36 }.
% 19.99/20.36 (82401) {G0,W12,D5,L2,V2,M2} { ! class_Fields_Ofield( X ),
% 19.99/20.36 c_Polynomial_Opoly__gcd( X, c_Groups_Oone__class_Oone(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Oone__class_Oone(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.36 (82402) {G0,W12,D5,L2,V2,M2} { ! class_Fields_Ofield( X ),
% 19.99/20.36 c_Polynomial_Opoly__gcd( X, Y, c_Groups_Oone__class_Oone(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Oone__class_Oone(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.36 (82403) {G0,W31,D6,L6,V4,M6} { ! class_Fields_Ofield( X ), ! hBOOL( hAPP(
% 19.99/20.36 hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 19.99/20.36 alpha26( X, Y, Z, T ), ! Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), ! T = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 19.99/20.36 (82404) {G0,W31,D6,L5,V4,M5} { ! class_Fields_Ofield( X ), ! hBOOL( hAPP(
% 19.99/20.36 hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 19.99/20.36 alpha26( X, Y, Z, T ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 19.99/20.36 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Oone__class_Oone( X ),
% 19.99/20.36 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 19.99/20.36 (82405) {G0,W14,D2,L3,V4,M3} { ! alpha26( X, Y, Z, T ), alpha27( X, Y, Z,
% 19.99/20.36 T ), alpha24( X, Y, T ) }.
% 19.99/20.36 (82406) {G0,W20,D4,L3,V4,M3} { ! alpha26( X, Y, Z, T ), alpha27( X, Y, Z,
% 19.99/20.36 T ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) )
% 19.99/20.36 = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (82407) {G0,W10,D2,L2,V4,M2} { ! alpha27( X, Y, Z, T ), alpha26( X, Y, Z,
% 19.99/20.36 T ) }.
% 19.99/20.36 (82408) {G0,W19,D4,L3,V4,M3} { ! alpha24( X, Y, T ), hAPP(
% 19.99/20.36 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), alpha26( X, Y, Z, T ) }.
% 19.99/20.36 (82409) {G0,W18,D6,L3,V4,M3} { ! alpha27( X, Y, Z, T ), ! hBOOL( hAPP(
% 19.99/20.36 hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), T ) ),
% 19.99/20.36 alpha28( X, Y, Z, T ) }.
% 19.99/20.36 (82410) {G0,W13,D6,L2,V4,M2} { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 19.99/20.36 ( tc_Polynomial_Opoly( X ) ), Z ), T ) ), alpha27( X, Y, Z, T ) }.
% 19.99/20.36 (82411) {G0,W10,D2,L2,V4,M2} { ! alpha28( X, Y, Z, T ), alpha27( X, Y, Z,
% 19.99/20.36 T ) }.
% 19.99/20.36 (82412) {G0,W17,D6,L2,V6,M2} { ! alpha28( X, Y, Z, T ), hBOOL( hAPP( hAPP
% 19.99/20.36 ( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), skol16( X, Y, U,
% 19.99/20.36 W ) ), Y ) ) }.
% 19.99/20.36 (82413) {G0,W17,D6,L2,V5,M2} { ! alpha28( X, Y, Z, T ), hBOOL( hAPP( hAPP
% 19.99/20.36 ( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), skol16( X, Y, U,
% 19.99/20.36 T ) ), T ) ) }.
% 19.99/20.36 (82414) {G0,W17,D6,L2,V4,M2} { ! alpha28( X, Y, Z, T ), ! hBOOL( hAPP(
% 19.99/20.36 hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), skol16( X, Y
% 19.99/20.36 , Z, T ) ), Z ) ) }.
% 19.99/20.36 (82415) {G0,W29,D6,L4,V5,M4} { ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), U ), Y ) ), ! hBOOL
% 19.99/20.36 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), U ),
% 19.99/20.36 T ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 19.99/20.36 X ) ), U ), Z ) ), alpha28( X, Y, Z, T ) }.
% 19.99/20.36 (82416) {G0,W9,D4,L2,V3,M2} { ! alpha24( X, Y, Z ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.36 (82417) {G0,W9,D4,L2,V3,M2} { ! alpha24( X, Y, Z ), Z =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.36 (82418) {G0,W14,D4,L3,V3,M3} { ! Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), ! Z = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ), alpha24( X, Y, Z ) }.
% 19.99/20.36 (82419) {G0,W15,D5,L2,V3,M2} { ! class_Groups_Ozero( X ),
% 19.99/20.36 c_Polynomial_OpCons( X, Z, Y ) = c_Polynomial_OAbs__poly( X,
% 19.99/20.36 c_Nat_Onat_Onat__case( X, Z, c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 19.99/20.36 (82420) {G0,W9,D4,L2,V2,M2} { ! class_Groups_Ozero( X ),
% 19.99/20.36 c_Polynomial_OAbs__poly( X, c_Polynomial_Ocoeff( X, Y ) ) = Y }.
% 19.99/20.36 (82421) {G0,W21,D6,L2,V2,M2} { ! class_Fields_Ofield( X ),
% 19.99/20.36 c_Polynomial_Opoly__gcd( X, Y, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Polynomial_Opoly( X ) ) ) = c_Polynomial_Osmult( X,
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, hAPP( c_Polynomial_Ocoeff( X, Y ),
% 19.99/20.36 c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 19.99/20.36 (82422) {G0,W15,D3,L3,V5,M3} { ! class_Groups_Ozero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, c_Polynomial_Odegree( X, Y
% 19.99/20.36 ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, skol17( T, U, Z ) )
% 19.99/20.36 }.
% 19.99/20.36 (82423) {G0,W19,D4,L3,V3,M3} { ! class_Groups_Ozero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, c_Polynomial_Odegree( X, Y
% 19.99/20.36 ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ), skol17( X, Y, Z ) ) =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (82424) {G0,W13,D4,L2,V2,M2} { !
% 19.99/20.36 class_Rings_Odivision__ring__inverse__zero( X ),
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 19.99/20.36 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 19.99/20.36 (82425) {G0,W17,D4,L3,V2,M3} { ! class_Rings_Odivision__ring( X ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X,
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Oinverse( X,
% 19.99/20.36 Y ) ) }.
% 19.99/20.36 (82426) {G0,W29,D6,L4,V3,M4} { ! class_Rings_Odivision__ring( X ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 19.99/20.36 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 19.99/20.36 (82427) {G0,W23,D6,L3,V3,M3} { ! class_Rings_Odivision__ring( X ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X,
% 19.99/20.36 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 19.99/20.36 ) ), Z ) }.
% 19.99/20.36 (82428) {G0,W20,D3,L5,V3,M5} { ! class_Rings_Odivision__ring( X ), !
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = c_Groups_Ozero__class_Ozero
% 19.99/20.36 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 19.99/20.36 (82429) {G0,W12,D3,L3,V2,M3} { ! class_Rings_Odivision__ring( X ), !
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 19.99/20.36 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (82430) {G0,W13,D4,L3,V2,M3} { ! class_Rings_Odivision__ring( X ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X,
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = Y }.
% 19.99/20.36 (82431) {G0,W12,D3,L3,V2,M3} { ! class_Rings_Odivision__ring( X ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Oinverse( X,
% 19.99/20.36 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (82432) {G0,W12,D3,L3,V2,M3} { !
% 19.99/20.36 class_Rings_Odivision__ring__inverse__zero( X ), !
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 19.99/20.36 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (82433) {G0,W12,D3,L3,V2,M3} { !
% 19.99/20.36 class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 19.99/20.36 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (82434) {G0,W9,D4,L2,V1,M2} { ! class_Rings_Odivision__ring__inverse__zero
% 19.99/20.36 ( X ), c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (82435) {G0,W19,D6,L2,V3,M2} { !
% 19.99/20.36 class_Rings_Odivision__ring__inverse__zero( X ),
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 19.99/20.36 ) ), Y ) }.
% 19.99/20.36 (82436) {G0,W12,D3,L3,V3,M3} { !
% 19.99/20.36 class_Rings_Odivision__ring__inverse__zero( X ), !
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 19.99/20.36 (82437) {G0,W12,D3,L3,V3,M3} { !
% 19.99/20.36 class_Rings_Odivision__ring__inverse__zero( X ), !
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 19.99/20.36 (82438) {G0,W12,D3,L3,V3,M3} { !
% 19.99/20.36 class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 19.99/20.36 (82439) {G0,W9,D4,L2,V2,M2} { ! class_Rings_Odivision__ring__inverse__zero
% 19.99/20.36 ( X ), c_Rings_Oinverse__class_Oinverse( X,
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = Y }.
% 19.99/20.36 (82440) {G0,W9,D4,L2,V1,M2} { ! class_Rings_Odivision__ring( X ),
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Oone__class_Oone( X ) ) =
% 19.99/20.36 c_Groups_Oone__class_Oone( X ) }.
% 19.99/20.36 (82441) {G0,W16,D5,L3,V3,M3} { ! class_Rings_Odivision__ring( X ), ! hAPP
% 19.99/20.36 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 19.99/20.36 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Z )
% 19.99/20.36 = Y }.
% 19.99/20.36 (82442) {G0,W37,D7,L4,V3,M4} { ! class_Rings_Odivision__ring( X ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Oinverse( X, Y )
% 19.99/20.36 , c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 19.99/20.36 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 19.99/20.36 (82443) {G0,W17,D5,L3,V2,M3} { ! class_Rings_Odivision__ring( X ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Y ), c_Rings_Oinverse__class_Oinverse
% 19.99/20.36 ( X, Y ) ) = c_Groups_Oone__class_Oone( X ) }.
% 19.99/20.36 (82444) {G0,W17,D5,L3,V2,M3} { ! class_Rings_Odivision__ring( X ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 19.99/20.36 Y ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 19.99/20.36 (82445) {G0,W26,D4,L4,V6,M4} { ! class_Fields_Ofield( X ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), ! c_Polynomial_Opdivmod__rel( X, W, U,
% 19.99/20.36 T, Z ), c_Polynomial_Opdivmod__rel( X, W, c_Polynomial_Osmult( X, Y, U )
% 19.99/20.36 , c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, Y ), T ),
% 19.99/20.36 Z ) }.
% 19.99/20.36 (82446) {G0,W19,D3,L4,V2,M4} { ! class_Fields_Olinordered__field( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 19.99/20.36 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 19.99/20.36 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 19.99/20.36 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 19.99/20.36 (82447) {G0,W19,D3,L4,V2,M4} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 19.99/20.36 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq(
% 19.99/20.36 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 19.99/20.36 X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 19.99/20.36 (82448) {G0,W14,D3,L3,V2,M3} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X
% 19.99/20.36 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 19.99/20.36 (82449) {G0,W14,D3,L3,V2,M3} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 19.99/20.36 ), c_Groups_Oone__class_Oone( X ) ) }.
% 19.99/20.36 (82450) {G0,W9,D4,L2,V1,M2} { ! class_Fields_Ofield__inverse__zero( X ),
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (82451) {G0,W21,D6,L2,V3,M2} { ! class_Fields_Ofield__inverse__zero( X ),
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 19.99/20.36 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 19.99/20.36 (82452) {G0,W12,D3,L3,V2,M3} { ! class_Fields_Ofield__inverse__zero( X ),
% 19.99/20.36 ! c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X
% 19.99/20.36 ), Y = c_Groups_Oone__class_Oone( X ) }.
% 19.99/20.36 (82453) {G0,W12,D3,L3,V2,M3} { ! class_Fields_Ofield__inverse__zero( X ),
% 19.99/20.36 ! Y = c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X
% 19.99/20.36 , Y ) = c_Groups_Oone__class_Oone( X ) }.
% 19.99/20.36 (82454) {G0,W14,D3,L3,V2,M3} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 19.99/20.36 ) }.
% 19.99/20.36 (82455) {G0,W14,D3,L3,V2,M3} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 19.99/20.36 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 19.99/20.36 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 19.99/20.36 (82456) {G0,W14,D3,L3,V2,M3} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 19.99/20.36 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 ) }.
% 19.99/20.36 (82457) {G0,W14,D3,L3,V2,M3} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 ), c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 19.99/20.36 ) ) }.
% 19.99/20.36 (82458) {G0,W19,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Z
% 19.99/20.36 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 19.99/20.36 (82459) {G0,W19,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Z
% 19.99/20.36 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 19.99/20.36 (82460) {G0,W18,D3,L4,V2,M4} { ! class_Fields_Olinordered__field( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 19.99/20.36 ), c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 19.99/20.36 X ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 19.99/20.36 ) ) }.
% 19.99/20.36 (82461) {G0,W19,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, c_Rings_Oinverse__class_Oinverse( X, Y ),
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 19.99/20.36 (82462) {G0,W19,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, c_Rings_Oinverse__class_Oinverse( X, Y ),
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 19.99/20.36 (82463) {G0,W14,D3,L3,V2,M3} { ! class_Fields_Olinordered__field( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 19.99/20.36 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 19.99/20.36 (82464) {G0,W18,D3,L4,V2,M4} { ! class_Fields_Olinordered__field( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 19.99/20.36 (82465) {G0,W14,D3,L3,V2,M3} { ! class_Fields_Olinordered__field( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 19.99/20.36 (82466) {G0,W14,D3,L3,V2,M3} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 19.99/20.36 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 19.99/20.36 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 19.99/20.36 (82467) {G0,W14,D3,L3,V2,M3} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 19.99/20.36 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 19.99/20.36 (82468) {G0,W14,D3,L3,V2,M3} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 19.99/20.36 (82469) {G0,W14,D3,L3,V2,M3} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 19.99/20.36 (82470) {G0,W19,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 19.99/20.36 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 19.99/20.36 (82471) {G0,W19,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 19.99/20.36 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 19.99/20.36 (82472) {G0,W19,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 19.99/20.36 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 19.99/20.36 (82473) {G0,W19,D3,L4,V3,M4} { ! class_Fields_Olinordered__field( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 19.99/20.36 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 19.99/20.36 (82474) {G0,W19,D3,L4,V2,M4} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 19.99/20.36 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 19.99/20.36 , Y ) }.
% 19.99/20.36 (82475) {G0,W14,D3,L3,V2,M3} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 ), c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oone__class_Oone( X )
% 19.99/20.36 ) }.
% 19.99/20.36 (82476) {G0,W14,D3,L3,V2,M3} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 19.99/20.36 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse
% 19.99/20.36 ( X, Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 19.99/20.36 (82477) {G0,W37,D7,L4,V3,M4} { ! class_Fields_Ofield( X ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Oinverse( X, Y )
% 19.99/20.36 , c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 19.99/20.36 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 19.99/20.36 (82478) {G0,W14,D3,L3,V2,M3} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 19.99/20.36 (82479) {G0,W14,D3,L3,V2,M3} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 19.99/20.36 (82480) {G0,W19,D3,L4,V2,M4} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 19.99/20.36 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 19.99/20.36 (82481) {G0,W19,D3,L4,V2,M4} { ! class_Fields_Olinordered__field( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 19.99/20.36 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 19.99/20.36 (82482) {G0,W17,D5,L3,V2,M3} { ! class_Fields_Ofield( X ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 19.99/20.36 Y ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 19.99/20.36 (82483) {G0,W14,D3,L3,V2,M3} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 19.99/20.36 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 19.99/20.36 (82484) {G0,W14,D3,L3,V2,M3} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 19.99/20.36 }.
% 19.99/20.36 (82485) {G0,W19,D3,L4,V2,M4} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 19.99/20.36 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 19.99/20.36 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 19.99/20.36 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 19.99/20.36 (82486) {G0,W24,D6,L3,V3,M3} { ! class_Fields_Ofield( X ), ! Z =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 19.99/20.36 c_Polynomial_Opoly__gcd( X, Y, Z ) = c_Polynomial_Osmult( X,
% 19.99/20.36 c_Rings_Oinverse__class_Oinverse( X, hAPP( c_Polynomial_Ocoeff( X, Y ),
% 19.99/20.36 c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 19.99/20.36 (82487) {G0,W20,D5,L3,V3,M3} { ! class_Fields_Ofield( X ), Z =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 19.99/20.36 c_Polynomial_Opoly__gcd( X, Y, Z ) = c_Polynomial_Opoly__gcd( X, Z,
% 19.99/20.36 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 19.99/20.36 (82488) {G0,W14,D3,L3,V5,M3} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 19.99/20.36 skol18( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 19.99/20.36 (82489) {G0,W14,D3,L3,V5,M3} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( X, skol18( X, T, U ),
% 19.99/20.36 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 19.99/20.36 , Y ) }.
% 19.99/20.36 (82490) {G0,W18,D5,L3,V3,M3} { !
% 19.99/20.36 class_Fields_Olinordered__field__inverse__zero( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), skol18( X, Y, Z ) ), Z ), Y ),
% 19.99/20.36 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 19.99/20.36 (82491) {G0,W18,D5,L2,V3,M2} { ! class_Divides_Oring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 19.99/20.36 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ouminus__class_Ouminus( X,
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 19.99/20.36 (82492) {G0,W24,D4,L3,V4,M3} { ! class_Divides_Oring__div( X ), !
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, T, Z ) = c_Divides_Odiv__class_Omod( X, Y
% 19.99/20.36 , Z ), c_Divides_Odiv__class_Omod( X, c_Groups_Ouminus__class_Ouminus( X
% 19.99/20.36 , T ), Z ) = c_Divides_Odiv__class_Omod( X,
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 19.99/20.36 (82493) {G0,W19,D5,L2,V3,M2} { ! class_Fields_Ofield( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ),
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 19.99/20.36 (82494) {G0,W16,D5,L2,V3,M2} { ! class_Fields_Ofield( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z,
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 19.99/20.36 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 19.99/20.36 (82495) {G0,W20,D4,L3,V4,M3} { ! class_Fields_Ofield( X ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ), c_Divides_Odiv__class_Omod(
% 19.99/20.36 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Y, Z ) ) =
% 19.99/20.36 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, Z ) }.
% 19.99/20.36 (82496) {G0,W17,D4,L3,V3,M3} { ! class_Fields_Ofield( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 19.99/20.36 , c_Polynomial_Odegree( X, Y ) ), c_Divides_Odiv__class_Omod(
% 19.99/20.36 tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 19.99/20.36 (82497) {G0,W19,D5,L2,V4,M2} { ! class_Fields_Ofield( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 19.99/20.36 ( X, T, Z ), Y ) = c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Omod
% 19.99/20.36 ( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 19.99/20.36 (82498) {G0,W15,D4,L3,V5,M3} { ! class_Fields_Ofield( X ), !
% 19.99/20.36 c_Polynomial_Opdivmod__rel( X, T, Z, U, Y ), c_Divides_Odiv__class_Omod(
% 19.99/20.36 tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 19.99/20.36 (82499) {G0,W14,D4,L2,V3,M2} { ! class_Divides_Osemiring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, c_Divides_Odiv__class_Omod( X, Z, Y ), Y )
% 19.99/20.36 = c_Divides_Odiv__class_Omod( X, Z, Y ) }.
% 19.99/20.36 (82500) {G0,W26,D5,L4,V4,M4} { ! class_Divides_Osemiring__div( X ), !
% 19.99/20.36 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), T ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, Z, Y ) ) ), ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( X ), T ), Y ) ), hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( X ), T ), Z ) ) }.
% 19.99/20.36 (82501) {G0,W26,D5,L4,V4,M4} { ! class_Divides_Osemiring__div( X ), !
% 19.99/20.36 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL(
% 19.99/20.36 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP
% 19.99/20.36 ( c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, Y, T
% 19.99/20.36 ) ) ) }.
% 19.99/20.36 (82502) {G0,W21,D5,L3,V4,M3} { ! class_Divides_Osemiring__div( X ), !
% 19.99/20.36 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, c_Divides_Odiv__class_Omod( X, T, Y ), Z )
% 19.99/20.36 = c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 19.99/20.36 (82503) {G0,W26,D5,L4,V4,M4} { ! class_Divides_Osemiring__div( X ), !
% 19.99/20.36 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL(
% 19.99/20.36 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, T, Y ) ) ), hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 19.99/20.36 (82504) {G0,W26,D5,L4,V4,M4} { ! class_Divides_Osemiring__div( X ), !
% 19.99/20.36 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL(
% 19.99/20.36 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP
% 19.99/20.36 ( c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, T, Y
% 19.99/20.36 ) ) ) }.
% 19.99/20.36 (82505) {G0,W16,D5,L3,V3,M3} { ! class_Divides_Osemiring__div( X ), !
% 19.99/20.36 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 }.
% 19.99/20.36 (82506) {G0,W16,D5,L3,V3,M3} { ! class_Divides_Osemiring__div( X ), !
% 19.99/20.36 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 }.
% 19.99/20.36 (82507) {G0,W16,D5,L3,V3,M3} { ! class_Divides_Osemiring__div( X ), !
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 19.99/20.36 (82508) {G0,W10,D4,L2,V2,M2} { ! class_Divides_Osemiring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, c_Groups_Ozero__class_Ozero( X ), Y ) =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (82509) {G0,W9,D4,L2,V2,M2} { ! class_Divides_Osemiring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, Y, c_Groups_Ozero__class_Ozero( X ) ) = Y
% 19.99/20.36 }.
% 19.99/20.36 (82510) {G0,W9,D3,L2,V2,M2} { ! class_Divides_Osemiring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 19.99/20.36 }.
% 19.99/20.36 (82511) {G0,W10,D4,L2,V2,M2} { ! class_Divides_Osemiring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, Y, c_Groups_Oone__class_Oone( X ) ) =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (82512) {G0,W14,D6,L2,V3,M2} { ! class_Divides_Osemiring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), Z ), Y ), Z ) = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (82513) {G0,W14,D6,L2,V3,M2} { ! class_Divides_Osemiring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), Z ), Y ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.36 (82514) {G0,W24,D6,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), T ), Z ), Y ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 19.99/20.36 , Y ) ), Y ) }.
% 19.99/20.36 (82515) {G0,W24,D6,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), T ), Z ), Y ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 19.99/20.36 ), Z ), Y ) }.
% 19.99/20.36 (82516) {G0,W27,D6,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), T ), Z ), Y ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 19.99/20.36 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 19.99/20.36 (82517) {G0,W26,D6,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y )
% 19.99/20.36 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, Z, Y ) ) }.
% 19.99/20.36 (82518) {G0,W26,D6,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z )
% 19.99/20.36 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ) }.
% 19.99/20.36 (82519) {G0,W24,D6,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ), Z ) =
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), T ), Y ), Z ) }.
% 19.99/20.36 (82520) {G0,W39,D6,L4,V6,M4} { ! class_Divides_Osemiring__div( X ), !
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, T, Z ) = c_Divides_Odiv__class_Omod( X, Y
% 19.99/20.36 , Z ), ! c_Divides_Odiv__class_Omod( X, W, Z ) =
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, U, Z ), c_Divides_Odiv__class_Omod( X,
% 19.99/20.36 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), W ), Z ) =
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.36 ( X ), Y ), U ), Z ) }.
% 19.99/20.36 (82521) {G0,W14,D4,L2,V3,M2} { ! class_Divides_Osemiring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Z, Y ), Y
% 19.99/20.36 ) = c_Divides_Odiv__class_Omod( X, Z, Y ) }.
% 19.99/20.36 (82522) {G0,W14,D4,L2,V3,M2} { ! class_Divides_Osemiring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Z, Y ), Z
% 19.99/20.36 ) = c_Divides_Odiv__class_Omod( X, Y, Z ) }.
% 19.99/20.36 (82523) {G0,W20,D5,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y
% 19.99/20.36 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T,
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 19.99/20.36 (82524) {G0,W20,D5,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y
% 19.99/20.36 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 19.99/20.36 (82525) {G0,W23,D5,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y
% 19.99/20.36 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 19.99/20.36 Y ) ), Y ) }.
% 19.99/20.36 (82526) {G0,W20,D5,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T,
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) = c_Divides_Odiv__class_Omod
% 19.99/20.36 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 19.99/20.36 (82527) {G0,W20,D5,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, T, Z ), Y ), Z ) =
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z
% 19.99/20.36 ) }.
% 19.99/20.36 (82528) {G0,W35,D4,L4,V6,M4} { ! class_Divides_Osemiring__div( X ), !
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, T, Z ) = c_Divides_Odiv__class_Omod( X, Y
% 19.99/20.36 , Z ), ! c_Divides_Odiv__class_Omod( X, W, Z ) =
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, U, Z ), c_Divides_Odiv__class_Omod( X,
% 19.99/20.36 c_Groups_Oplus__class_Oplus( X, T, W ), Z ) = c_Divides_Odiv__class_Omod
% 19.99/20.36 ( X, c_Groups_Oplus__class_Oplus( X, Y, U ), Z ) }.
% 19.99/20.36 (82529) {G0,W19,D7,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, hAPP(
% 19.99/20.36 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 19.99/20.36 (82530) {G0,W19,D7,L2,V4,M2} { ! class_Divides_Osemiring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, hAPP(
% 19.99/20.36 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 19.99/20.36 (82531) {G0,W20,D5,L3,V3,M3} { ! class_Fields_Ofield( X ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 19.99/20.36 c_Polynomial_Opoly__gcd( X, Z, Y ) = c_Polynomial_Opoly__gcd( X, Y,
% 19.99/20.36 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 19.99/20.36 (82532) {G0,W28,D5,L4,V3,M4} { ! class_Fields_Ofield( X ), Y =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 19.99/20.36 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) ),
% 19.99/20.36 c_Polynomial_Odegree( X, Y ) ) }.
% 19.99/20.36 (82533) {G0,W29,D7,L3,V3,M3} { ! class_Groups_Omonoid__mult( X ), !
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 19.99/20.36 tc_Nat_Onat ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP
% 19.99/20.36 ( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 19.99/20.36 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 19.99/20.36 ( tc_Nat_Onat ) ) ) ), Z ) = hAPP( hAPP( c_Power_Opower__class_Opower( X
% 19.99/20.36 ), Z ), Y ) }.
% 19.99/20.36 (82534) {G0,W23,D5,L4,V4,M4} { ! class_Orderings_Oorder( X ), !
% 19.99/20.36 c_Orderings_Oorder_Omono( tc_Nat_Onat, X, c_Rings_Odvd__class_Odvd(
% 19.99/20.36 tc_Nat_Onat ), Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 19.99/20.36 tc_Nat_Onat ), T ), Z ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Y
% 19.99/20.36 , T ), hAPP( Y, Z ) ) }.
% 19.99/20.36 (82535) {G0,W16,D5,L1,V2,M1} { c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 19.99/20.36 ( tc_Int_Oint, Y, X ) ), X ) = c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 19.99/20.36 (82536) {G0,W15,D4,L1,V2,M1} { c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 19.99/20.36 ( tc_Int_Oint, Y, X ) ) }.
% 19.99/20.36 (82537) {G0,W15,D5,L1,V2,M1} { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y
% 19.99/20.36 , c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 19.99/20.36 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) )
% 19.99/20.36 }.
% 19.99/20.36 (82538) {G0,W16,D4,L2,V2,M2} { c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 19.99/20.36 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 19.99/20.36 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 19.99/20.36 (82539) {G0,W16,D4,L2,V2,M2} { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y
% 19.99/20.36 , c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 19.99/20.36 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 19.99/20.36 (82540) {G0,W35,D4,L4,V6,M4} { ! class_Divides_Oring__div( X ), !
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, T, Z ) = c_Divides_Odiv__class_Omod( X, Y
% 19.99/20.36 , Z ), ! c_Divides_Odiv__class_Omod( X, W, Z ) =
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, U, Z ), c_Divides_Odiv__class_Omod( X,
% 19.99/20.36 c_Groups_Ominus__class_Ominus( X, T, W ), Z ) =
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y, U ),
% 19.99/20.36 Z ) }.
% 19.99/20.36 (82541) {G0,W23,D5,L2,V4,M2} { ! class_Divides_Oring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, Z ),
% 19.99/20.36 Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 19.99/20.36 Y ) ), Y ) }.
% 19.99/20.36 (82542) {G0,W20,D5,L2,V4,M2} { ! class_Divides_Oring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, Z ),
% 19.99/20.36 Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 19.99/20.36 (82543) {G0,W20,D5,L2,V4,M2} { ! class_Divides_Oring__div( X ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, Z ),
% 19.99/20.36 Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T
% 19.99/20.36 , c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 19.99/20.36 (82544) {G0,W14,D5,L1,V2,M1} { c_Divides_Odiv__class_Omod( tc_Nat_Onat,
% 19.99/20.36 c_Nat_OSuc( Y ), X ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat,
% 19.99/20.36 c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 19.99/20.36 (82545) {G0,W24,D5,L3,V3,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), c_Divides_Odiv__class_Omod
% 19.99/20.36 ( tc_Int_Oint, Y, X ) ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 19.99/20.36 ( tc_Int_Oint ), Z ), X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 19.99/20.36 ( tc_Int_Oint ), Z ), Y ) ) }.
% 19.99/20.36 (82546) {G0,W24,D5,L3,V3,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.36 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.36 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), Z ) ), hBOOL( hAPP( hAPP
% 19.99/20.36 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) ) }.
% 19.99/20.36 (82547) {G0,W22,D6,L1,V3,M1} { c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 19.99/20.36 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) ), X ), Y ) =
% 19.99/20.36 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 19.99/20.36 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y ) }.
% 19.99/20.36 (82548) {G0,W15,D4,L2,V2,M2} { ! c_Nat_OSuc( c_Divides_Odiv__class_Omod(
% 19.99/20.36 tc_Nat_Onat, Y, X ) ) = X, c_Divides_Odiv__class_Omod( tc_Nat_Onat,
% 19.99/20.36 c_Nat_OSuc( Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.36 (82549) {G0,W18,D4,L2,V2,M2} { c_Nat_OSuc( c_Divides_Odiv__class_Omod(
% 19.99/20.36 tc_Nat_Onat, Y, X ) ) = X, c_Divides_Odiv__class_Omod( tc_Nat_Onat,
% 19.99/20.36 c_Nat_OSuc( Y ), X ) = c_Nat_OSuc( c_Divides_Odiv__class_Omod(
% 19.99/20.36 tc_Nat_Onat, Y, X ) ) }.
% 19.99/20.36 (82550) {G0,W9,D5,L1,V1,M1} { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X,
% 19.99/20.36 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.36 (82551) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Omod(
% 19.99/20.36 tc_Nat_Onat, Y, X ), X ) }.
% 19.99/20.36 (82552) {G0,W17,D5,L2,V2,M2} { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat,
% 19.99/20.36 Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol19( X, Y ) ) }.
% 19.99/20.36 (82553) {G0,W15,D5,L2,V3,M2} { ! Y = hAPP( hAPP(
% 19.99/20.36 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ),
% 19.99/20.36 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 19.99/20.36 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.36 (82554) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.36 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 19.99/20.36 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 19.99/20.36 tc_Int_Oint, Y, X ), X ) }.
% 19.99/20.36 (82555) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.37 tc_Int_Oint, X, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 19.99/20.37 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 19.99/20.37 ( tc_Int_Oint, Y, X ) ) }.
% 19.99/20.37 (82556) {G0,W10,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.37 tc_Nat_Onat, Y, X ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y
% 19.99/20.37 }.
% 19.99/20.37 (82557) {G0,W16,D4,L2,V2,M2} { c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.37 , Y, X ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 19.99/20.37 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 19.99/20.37 tc_Nat_Onat, Y, X ), X ) }.
% 19.99/20.37 (82558) {G0,W16,D4,L2,V2,M2} { c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.37 , Y, X ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 19.99/20.37 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 19.99/20.37 tc_Nat_Onat, Y, X ), X ) }.
% 19.99/20.37 (82559) {G0,W10,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.37 tc_Nat_Onat, Y, X ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y
% 19.99/20.37 }.
% 19.99/20.37 (82560) {G0,W8,D4,L1,V1,M1} { c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 19.99/20.37 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ) =
% 19.99/20.37 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 19.99/20.37 (82561) {G0,W7,D3,L1,V1,M1} { c_Divides_Odiv__class_Omod( tc_Int_Oint, X,
% 19.99/20.37 X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 19.99/20.37 (82562) {G0,W22,D6,L1,V3,M1} { c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 19.99/20.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 19.99/20.37 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 19.99/20.37 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 19.99/20.37 (82563) {G0,W22,D6,L1,V3,M1} { c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 19.99/20.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 19.99/20.37 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 19.99/20.37 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 19.99/20.37 (82564) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.37 tc_Nat_Onat ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 19.99/20.37 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.37 (82565) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.37 tc_Nat_Onat ), Z ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 19.99/20.37 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 19.99/20.37 (82566) {G0,W17,D5,L2,V2,M2} { ! c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 19.99/20.37 Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol20( X, Y ) ) }.
% 19.99/20.37 (82567) {G0,W15,D5,L2,V3,M2} { ! Y = hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ),
% 19.99/20.37 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 19.99/20.37 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 19.99/20.37 (82568) {G0,W7,D3,L1,V2,M1} { c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), Y ) }.
% 19.99/20.37 (82569) {G0,W16,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, Y, X ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) =
% 19.99/20.37 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 19.99/20.37 tc_Nat_Onat, X, Y ), Y ) }.
% 19.99/20.37 (82570) {G0,W18,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 19.99/20.37 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 19.99/20.37 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 19.99/20.37 tc_Int_Oint, X, Y ) ) }.
% 19.99/20.37 (82571) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 19.99/20.37 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 19.99/20.37 (82572) {G0,W17,D7,L1,V3,M1} { c_Divides_Odiv__class_Omod( tc_Nat_Onat,
% 19.99/20.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ), Y ) =
% 19.99/20.37 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 19.99/20.37 (82573) {G0,W37,D6,L3,V6,M3} { ! class_Rings_Oordered__ring( X ), !
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 19.99/20.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 19.99/20.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.37 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 19.99/20.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.37 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 19.99/20.37 (82574) {G0,W37,D6,L3,V6,M3} { ! class_Rings_Oordered__ring( X ), !
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 19.99/20.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 19.99/20.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 19.99/20.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.37 ( X ), Z ), U ), Y ) ) }.
% 19.99/20.37 (82575) {G0,W37,D6,L3,V6,M3} { ! class_Rings_Oordered__ring( X ), !
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 19.99/20.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 19.99/20.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.37 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 19.99/20.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.37 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 19.99/20.37 (82576) {G0,W37,D6,L3,V6,M3} { ! class_Rings_Oordered__ring( X ), !
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 19.99/20.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ),
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 19.99/20.37 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 19.99/20.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.37 ( X ), Z ), U ), Y ) ) }.
% 19.99/20.37 (82577) {G0,W19,D5,L2,V5,M2} { ! class_Groups_Ominus( X ), hAPP(
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_fun( U, X ), T, Z ), Y ) =
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ), hAPP( Z, Y ) ) }.
% 19.99/20.37 (82578) {G0,W14,D5,L1,V2,M1} { c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 19.99/20.37 , Y, c_Nat_OSuc( X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 19.99/20.37 ( tc_Nat_Onat ) ), X ) }.
% 19.99/20.37 (82579) {G0,W8,D4,L1,V1,M1} { c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 19.99/20.37 c_Nat_OSuc( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 19.99/20.37 (82580) {G0,W11,D4,L1,V2,M1} { c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 19.99/20.37 , c_Nat_OSuc( Y ), c_Nat_OSuc( X ) ) = c_Groups_Ominus__class_Ominus(
% 19.99/20.37 tc_Nat_Onat, Y, X ) }.
% 19.99/20.37 (82581) {G0,W17,D5,L1,V3,M1} { c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 19.99/20.37 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ),
% 19.99/20.37 c_Nat_OSuc( X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 19.99/20.37 (82582) {G0,W17,D3,L4,V5,M4} { ! class_Groups_Oab__group__add( X ), !
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 19.99/20.37 ( X, Z, Y ), ! U = T, Z = Y }.
% 19.99/20.37 (82583) {G0,W17,D3,L4,V5,M4} { ! class_Groups_Oab__group__add( X ), !
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 19.99/20.37 ( X, Z, Y ), ! Z = Y, U = T }.
% 19.99/20.37 (82584) {G0,W21,D4,L2,V4,M2} { ! class_Groups_Oab__group__add( X ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 19.99/20.37 c_Polynomial_Omonom( X, T, Z ), c_Polynomial_Omonom( X, Y, Z ) ) =
% 19.99/20.37 c_Polynomial_Omonom( X, c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 19.99/20.37 (82585) {G0,W24,D6,L2,V4,M2} { ! class_Groups_Oab__group__add( X ), hAPP(
% 19.99/20.37 c_Polynomial_Ocoeff( X, c_Groups_Ominus__class_Ominus(
% 19.99/20.37 tc_Polynomial_Opoly( X ), T, Z ) ), Y ) = c_Groups_Ominus__class_Ominus(
% 19.99/20.37 X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ), hAPP( c_Polynomial_Ocoeff( X,
% 19.99/20.37 Z ), Y ) ) }.
% 19.99/20.37 (82586) {G0,W21,D4,L2,V4,M2} { ! class_Rings_Ocomm__ring( X ),
% 19.99/20.37 c_Polynomial_Osmult( X, c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 19.99/20.37 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 19.99/20.37 (82587) {G0,W24,D6,L2,V4,M2} { ! class_Rings_Ocomm__ring( X ), hAPP(
% 19.99/20.37 c_Polynomial_Opoly( X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly
% 19.99/20.37 ( X ), T, Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP(
% 19.99/20.37 c_Polynomial_Opoly( X, T ), Y ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) )
% 19.99/20.37 }.
% 19.99/20.37 (82588) {G0,W25,D5,L2,V5,M2} { ! class_Groups_Oab__group__add( X ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 19.99/20.37 c_Polynomial_OpCons( X, U, T ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 19.99/20.37 c_Polynomial_OpCons( X, c_Groups_Ominus__class_Ominus( X, U, Z ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 19.99/20.37 (82589) {G0,W15,D4,L1,V3,M1} { c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 19.99/20.37 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) =
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 19.99/20.37 ( tc_Nat_Onat, Z, X ), Y ) }.
% 19.99/20.37 (82590) {G0,W24,D5,L3,V3,M3} { ! hBOOL( hAPP( hAPP(
% 19.99/20.37 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), ! hBOOL( hAPP( hAPP
% 19.99/20.37 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z ) ), hBOOL( hAPP( hAPP
% 19.99/20.37 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) ) }.
% 19.99/20.37 (82591) {G0,W26,D5,L4,V4,M4} { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL
% 19.99/20.37 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP(
% 19.99/20.37 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 19.99/20.37 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ominus__class_Ominus( X, Y,
% 19.99/20.37 T ) ) ) }.
% 19.99/20.37 (82592) {G0,W28,D5,L4,V3,M4} { ! hBOOL( hAPP( hAPP(
% 19.99/20.37 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), ! hBOOL( hAPP(
% 19.99/20.37 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ), !
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), hBOOL( hAPP( hAPP
% 19.99/20.37 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 19.99/20.37 (82593) {G0,W28,D5,L4,V3,M4} { ! hBOOL( hAPP( hAPP(
% 19.99/20.37 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), ! hBOOL( hAPP(
% 19.99/20.37 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), !
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), hBOOL( hAPP( hAPP
% 19.99/20.37 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 19.99/20.37 (82594) {G0,W18,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.37 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 19.99/20.37 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 19.99/20.37 (82595) {G0,W22,D3,L4,V3,M4} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 19.99/20.37 , Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 19.99/20.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 19.99/20.37 (82596) {G0,W22,D3,L4,V3,M4} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 19.99/20.37 , Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 19.99/20.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 19.99/20.37 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 19.99/20.37 ) }.
% 19.99/20.37 (82597) {G0,W15,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, Y, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 19.99/20.37 c_Nat_OSuc( X ), Y ) = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 19.99/20.37 tc_Nat_Onat, X, Y ) ) }.
% 19.99/20.37 (82598) {G0,W11,D3,L2,V2,M2} { ! c_Groups_Ominus__class_Ominus(
% 19.99/20.37 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 19.99/20.37 (82599) {G0,W11,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, Y, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 19.99/20.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.37 (82600) {G0,W11,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, Y, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 19.99/20.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.37 (82601) {G0,W8,D3,L1,V2,M1} { c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 19.99/20.37 (82602) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.37 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 19.99/20.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 19.99/20.37 (82603) {G0,W12,D3,L2,V2,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.37 tc_Nat_Onat, X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus
% 19.99/20.37 ( tc_Nat_Onat, Y, X ) ) }.
% 19.99/20.37 (82604) {G0,W17,D3,L3,V2,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.37 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ), !
% 19.99/20.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 19.99/20.37 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 19.99/20.37 (82605) {G0,W35,D6,L3,V6,M3} { ! class_Rings_Oring( X ), !
% 19.99/20.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.37 ( X ), W ), U ), T ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ),
% 19.99/20.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.37 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ) = Y }.
% 19.99/20.37 (82606) {G0,W35,D6,L3,V6,M3} { ! class_Rings_Oring( X ), !
% 19.99/20.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.37 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ) = Y,
% 19.99/20.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.37 ( X ), W ), U ), T ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) }.
% 19.99/20.37 (82607) {G0,W35,D6,L3,V6,M3} { ! class_Rings_Oring( X ), !
% 19.99/20.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.37 ( X ), W ), U ), T ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ), T =
% 19.99/20.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.37 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) }.
% 19.99/20.37 (82608) {G0,W35,D6,L3,V6,M3} { ! class_Rings_Oring( X ), ! T =
% 19.99/20.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.37 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ),
% 19.99/20.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.37 ( X ), W ), U ), T ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) }.
% 19.99/20.37 (82609) {G0,W37,D6,L2,V5,M2} { ! class_Rings_Oring( X ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 19.99/20.37 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 19.99/20.37 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 19.99/20.37 Z ) ), Y ) ) }.
% 19.99/20.37 (82610) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.37 ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 19.99/20.37 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 19.99/20.37 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 19.99/20.37 (82611) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.37 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X
% 19.99/20.37 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 19.99/20.37 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 19.99/20.37 (82612) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.37 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 19.99/20.37 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 19.99/20.37 (82613) {G0,W14,D3,L3,V3,M3} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.37 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus
% 19.99/20.37 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 19.99/20.37 (82614) {G0,W18,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.37 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z )
% 19.99/20.37 , c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 19.99/20.37 (82615) {G0,W11,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.37 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ), X ) }.
% 19.99/20.37 (82616) {G0,W17,D3,L3,V2,M3} { ! c_Groups_Ominus__class_Ominus(
% 19.99/20.37 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 19.99/20.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 19.99/20.37 (82617) {G0,W7,D3,L1,V1,M1} { c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 19.99/20.37 X, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.37 (82618) {G0,W7,D4,L1,V1,M1} { c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 19.99/20.37 X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 19.99/20.37 (82619) {G0,W8,D4,L1,V1,M1} { c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 19.99/20.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) =
% 19.99/20.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 19.99/20.37 (82620) {G0,W19,D3,L4,V5,M4} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.37 ), ! c_Groups_Ominus__class_Ominus( X, U, T ) =
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 19.99/20.37 ( X, U, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 19.99/20.37 (82621) {G0,W19,D3,L4,V5,M4} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.37 ), ! c_Groups_Ominus__class_Ominus( X, U, T ) =
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 19.99/20.37 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, U, T ) }.
% 19.99/20.37 (82622) {G0,W9,D4,L2,V2,M2} { ! class_Groups_Ogroup__add( X ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Ozero__class_Ozero( X ) ) =
% 19.99/20.37 Y }.
% 19.99/20.37 (82623) {G0,W9,D3,L2,V2,M2} { ! class_Groups_Ogroup__add( X ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X
% 19.99/20.37 ) }.
% 19.99/20.37 (82624) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Oab__group__add( X ), ! Z =
% 19.99/20.37 Y, c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero
% 19.99/20.37 ( X ) }.
% 19.99/20.37 (82625) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Oab__group__add( X ), !
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 19.99/20.37 ), Z = Y }.
% 19.99/20.37 (82626) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), !
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 19.99/20.37 ), Z = Y }.
% 19.99/20.37 (82627) {G0,W12,D3,L3,V3,M3} { ! class_Groups_Ogroup__add( X ), ! Z = Y,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 19.99/20.37 ) }.
% 19.99/20.37 (82628) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 19.99/20.37 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 19.99/20.37 (82629) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 19.99/20.37 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 19.99/20.37 (82630) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 19.99/20.37 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) =
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 19.99/20.37 (82631) {G0,W26,D6,L2,V4,M2} { ! class_RealVector_Oreal__normed__algebra(
% 19.99/20.37 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) =
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 19.99/20.37 (82632) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.37 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X )
% 19.99/20.37 = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 19.99/20.37 (82633) {G0,W24,D6,L1,V3,M1} { hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.37 tc_Nat_Onat ), Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) )
% 19.99/20.37 = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 19.99/20.37 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 19.99/20.37 (82634) {G0,W19,D3,L4,V5,M4} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.37 ), ! c_Groups_Ominus__class_Ominus( X, U, T ) =
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, Z, Y ), !
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 19.99/20.37 (82635) {G0,W19,D3,L4,V5,M4} { ! class_Groups_Oordered__ab__group__add( X
% 19.99/20.37 ), ! c_Groups_Ominus__class_Ominus( X, U, T ) =
% 19.99/20.37 c_Groups_Ominus__class_Ominus( X, Z, Y ), !
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 19.99/20.37 (82636) {G0,W7,D3,L1,V2,M1} { c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 19.99/20.37 (82637) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 19.99/20.37 (82638) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 19.99/20.37 (82639) {G0,W13,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, Y, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 19.99/20.37 (82640) {G0,W20,D3,L4,V3,M4} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 19.99/20.37 , Z ), ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 19.99/20.37 (82641) {G0,W20,D3,L4,V3,M4} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 19.99/20.37 , Z ), ! X = Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 19.99/20.37 (82642) {G0,W23,D4,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 19.99/20.37 , Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) =
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 19.99/20.37 (82643) {G0,W22,D3,L4,V3,M4} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 19.99/20.37 , Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 19.99/20.37 (82644) {G0,W22,D3,L4,V3,M4} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 19.99/20.37 , Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 19.99/20.37 (82645) {G0,W19,D4,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, Y, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 19.99/20.37 tc_Nat_Onat, Z, Y ), X ) }.
% 19.99/20.37 (82646) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.37 tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 19.99/20.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 19.99/20.37 tc_Nat_Onat, Z, X ), Y ) }.
% 19.99/20.37 (82647) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless(
% 19.99/20.37 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y ),
% 19.99/20.37 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 19.99/20.37 (82648) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 19.99/20.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 19.99/20.37 (82649) {G0,W14,D3,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 19.99/20.37 (82650) {G0,W13,D4,L2,V2,M2} { c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 19.99/20.37 , Y, X ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 19.99/20.37 (82651) {G0,W14,D4,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, Y, X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 19.99/20.37 tc_Nat_Onat, X, Z ), Y ) ) }.
% 19.99/20.37 (82652) {G0,W13,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, Y, X ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 19.99/20.37 (82653) {G0,W19,D4,L2,V3,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, Y, X ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 19.99/20.37 tc_Nat_Onat, Z, X ), Y ) }.
% 19.99/20.37 (82654) {G0,W18,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 19.99/20.37 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 19.99/20.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 19.99/20.37 (82655) {G0,W18,D3,L3,V3,M3} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, Y, X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 19.99/20.37 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 19.99/20.37 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 19.99/20.37 (82656) {G0,W13,D4,L2,V2,M2} { ! c_Orderings_Oord__class_Oless__eq(
% 19.99/20.37 tc_Nat_Onat, Y, X ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 19.99/20.37 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Y ) = X }.
% 19.99/20.37 (82657) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Ocancel__comm__monoid__add( X
% 19.99/20.37 ), class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) )
% 19.99/20.37 }.
% 19.99/20.37 (82658) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__comm__monoid__add(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82659) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__comm__monoid__add(
% 19.99/20.37 tc_Nat_Onat ) }.
% 19.99/20.37 (82660) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__comm__monoid__add(
% 19.99/20.37 tc_Int_Oint ) }.
% 19.99/20.37 (82661) {G0,W6,D3,L2,V2,M2} { ! class_Lattices_Oboolean__algebra( X ),
% 19.99/20.37 class_Lattices_Oboolean__algebra( tc_fun( Y, X ) ) }.
% 19.99/20.37 (82662) {G0,W6,D3,L2,V2,M2} { ! class_Orderings_Opreorder( X ),
% 19.99/20.37 class_Orderings_Opreorder( tc_fun( Y, X ) ) }.
% 19.99/20.37 (82663) {G0,W6,D3,L2,V2,M2} { ! class_Orderings_Oorder( X ),
% 19.99/20.37 class_Orderings_Oorder( tc_fun( Y, X ) ) }.
% 19.99/20.37 (82664) {G0,W6,D3,L2,V2,M2} { ! class_Orderings_Oord( X ),
% 19.99/20.37 class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 19.99/20.37 (82665) {G0,W6,D3,L2,V2,M2} { ! class_Groups_Ouminus( X ),
% 19.99/20.37 class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 19.99/20.37 (82666) {G0,W6,D3,L2,V2,M2} { ! class_Groups_Ominus( X ),
% 19.99/20.37 class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 19.99/20.37 (82667) {G0,W2,D2,L1,V0,M1} {
% 19.99/20.37 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 19.99/20.37 tc_Int_Oint ) }.
% 19.99/20.37 (82668) {G0,W2,D2,L1,V0,M1} {
% 19.99/20.37 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 19.99/20.37 (82669) {G0,W2,D2,L1,V0,M1} {
% 19.99/20.37 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 19.99/20.37 (82670) {G0,W2,D2,L1,V0,M1} {
% 19.99/20.37 class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 19.99/20.37 (82671) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring__1__strict
% 19.99/20.37 ( tc_Int_Oint ) }.
% 19.99/20.37 (82672) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring__strict(
% 19.99/20.37 tc_Int_Oint ) }.
% 19.99/20.37 (82673) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__ab__semigroup__add(
% 19.99/20.37 tc_Int_Oint ) }.
% 19.99/20.37 (82674) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__comm__monoid__add(
% 19.99/20.37 tc_Int_Oint ) }.
% 19.99/20.37 (82675) {G0,W2,D2,L1,V0,M1} { class_Groups_Olinordered__ab__group__add(
% 19.99/20.37 tc_Int_Oint ) }.
% 19.99/20.37 (82676) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__ab__semigroup__add(
% 19.99/20.37 tc_Int_Oint ) }.
% 19.99/20.37 (82677) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__1__no__zero__divisors(
% 19.99/20.37 tc_Int_Oint ) }.
% 19.99/20.37 (82678) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__cancel__semiring(
% 19.99/20.37 tc_Int_Oint ) }.
% 19.99/20.37 (82679) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__ring__strict(
% 19.99/20.37 tc_Int_Oint ) }.
% 19.99/20.37 (82680) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__no__zero__divisors(
% 19.99/20.37 tc_Int_Oint ) }.
% 19.99/20.37 (82681) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__comm__semiring(
% 19.99/20.37 tc_Int_Oint ) }.
% 19.99/20.37 (82682) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring__1(
% 19.99/20.37 tc_Int_Oint ) }.
% 19.99/20.37 (82683) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__ab__group__add(
% 19.99/20.37 tc_Int_Oint ) }.
% 19.99/20.37 (82684) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__semigroup__add(
% 19.99/20.37 tc_Int_Oint ) }.
% 19.99/20.37 (82685) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring(
% 19.99/20.37 tc_Int_Oint ) }.
% 19.99/20.37 (82686) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semidom(
% 19.99/20.37 tc_Int_Oint ) }.
% 19.99/20.37 (82687) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__semigroup__mult(
% 19.99/20.37 tc_Int_Oint ) }.
% 19.99/20.37 (82688) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocomm__monoid__mult(
% 19.99/20.37 tc_Int_Oint ) }.
% 19.99/20.37 (82689) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__semigroup__add(
% 19.99/20.37 tc_Int_Oint ) }.
% 19.99/20.37 (82690) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__semiring( tc_Int_Oint
% 19.99/20.37 ) }.
% 19.99/20.37 (82691) {G0,W2,D2,L1,V0,M1} { class_Rings_Ono__zero__divisors( tc_Int_Oint
% 19.99/20.37 ) }.
% 19.99/20.37 (82692) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocomm__monoid__add( tc_Int_Oint
% 19.99/20.37 ) }.
% 19.99/20.37 (82693) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__ring( tc_Int_Oint )
% 19.99/20.37 }.
% 19.99/20.37 (82694) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__idom( tc_Int_Oint )
% 19.99/20.37 }.
% 19.99/20.37 (82695) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__1( tc_Int_Oint
% 19.99/20.37 ) }.
% 19.99/20.37 (82696) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__0( tc_Int_Oint
% 19.99/20.37 ) }.
% 19.99/20.37 (82697) {G0,W2,D2,L1,V0,M1} { class_Divides_Osemiring__div( tc_Int_Oint )
% 19.99/20.37 }.
% 19.99/20.37 (82698) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring( tc_Int_Oint )
% 19.99/20.37 }.
% 19.99/20.37 (82699) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__group__add( tc_Int_Oint )
% 19.99/20.37 }.
% 19.99/20.37 (82700) {G0,W2,D2,L1,V0,M1} { class_Rings_Ozero__neq__one( tc_Int_Oint )
% 19.99/20.37 }.
% 19.99/20.37 (82701) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__ring( tc_Int_Oint )
% 19.99/20.37 }.
% 19.99/20.37 (82702) {G0,W2,D2,L1,V0,M1} { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 19.99/20.37 (82703) {G0,W2,D2,L1,V0,M1} { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 19.99/20.37 (82704) {G0,W2,D2,L1,V0,M1} { class_Groups_Omonoid__mult( tc_Int_Oint )
% 19.99/20.37 }.
% 19.99/20.37 (82705) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__ring__1( tc_Int_Oint )
% 19.99/20.37 }.
% 19.99/20.37 (82706) {G0,W2,D2,L1,V0,M1} { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 19.99/20.37 (82707) {G0,W2,D2,L1,V0,M1} { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 19.99/20.37 (82708) {G0,W2,D2,L1,V0,M1} { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 19.99/20.37 (82709) {G0,W2,D2,L1,V0,M1} { class_Divides_Oring__div( tc_Int_Oint ) }.
% 19.99/20.37 (82710) {G0,W2,D2,L1,V0,M1} { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 19.99/20.37 (82711) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 19.99/20.37 (82712) {G0,W2,D2,L1,V0,M1} { class_Orderings_Oorder( tc_Int_Oint ) }.
% 19.99/20.37 (82713) {G0,W2,D2,L1,V0,M1} { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 19.99/20.37 (82714) {G0,W2,D2,L1,V0,M1} { class_Rings_Osemiring( tc_Int_Oint ) }.
% 19.99/20.37 (82715) {G0,W2,D2,L1,V0,M1} { class_Orderings_Oord( tc_Int_Oint ) }.
% 19.99/20.37 (82716) {G0,W2,D2,L1,V0,M1} { class_Groups_Ouminus( tc_Int_Oint ) }.
% 19.99/20.37 (82717) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__1( tc_Int_Oint ) }.
% 19.99/20.37 (82718) {G0,W2,D2,L1,V0,M1} { class_Groups_Ominus( tc_Int_Oint ) }.
% 19.99/20.37 (82719) {G0,W2,D2,L1,V0,M1} { class_Power_Opower( tc_Int_Oint ) }.
% 19.99/20.37 (82720) {G0,W2,D2,L1,V0,M1} { class_Groups_Ozero( tc_Int_Oint ) }.
% 19.99/20.37 (82721) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring( tc_Int_Oint ) }.
% 19.99/20.37 (82722) {G0,W2,D2,L1,V0,M1} { class_Rings_Oidom( tc_Int_Oint ) }.
% 19.99/20.37 (82723) {G0,W2,D2,L1,V0,M1} { class_Groups_Oone( tc_Int_Oint ) }.
% 19.99/20.37 (82724) {G0,W2,D2,L1,V0,M1} { class_Rings_Odvd( tc_Int_Oint ) }.
% 19.99/20.37 (82725) {G0,W2,D2,L1,V0,M1} {
% 19.99/20.37 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 19.99/20.37 tc_Nat_Onat ) }.
% 19.99/20.37 (82726) {G0,W2,D2,L1,V0,M1} {
% 19.99/20.37 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 19.99/20.37 (82727) {G0,W2,D2,L1,V0,M1} {
% 19.99/20.37 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 19.99/20.37 (82728) {G0,W2,D2,L1,V0,M1} {
% 19.99/20.37 class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 19.99/20.37 (82729) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring__strict(
% 19.99/20.37 tc_Nat_Onat ) }.
% 19.99/20.37 (82730) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__ab__semigroup__add(
% 19.99/20.37 tc_Nat_Onat ) }.
% 19.99/20.37 (82731) {G0,W2,D2,L1,V0,M1} { class_Groups_Oordered__comm__monoid__add(
% 19.99/20.37 tc_Nat_Onat ) }.
% 19.99/20.37 (82732) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__ab__semigroup__add(
% 19.99/20.37 tc_Nat_Onat ) }.
% 19.99/20.37 (82733) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__cancel__semiring(
% 19.99/20.37 tc_Nat_Onat ) }.
% 19.99/20.37 (82734) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__comm__semiring(
% 19.99/20.37 tc_Nat_Onat ) }.
% 19.99/20.37 (82735) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__semigroup__add(
% 19.99/20.37 tc_Nat_Onat ) }.
% 19.99/20.37 (82736) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semiring(
% 19.99/20.37 tc_Nat_Onat ) }.
% 19.99/20.37 (82737) {G0,W2,D2,L1,V0,M1} { class_Rings_Olinordered__semidom(
% 19.99/20.37 tc_Nat_Onat ) }.
% 19.99/20.37 (82738) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__semigroup__mult(
% 19.99/20.37 tc_Nat_Onat ) }.
% 19.99/20.37 (82739) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocomm__monoid__mult(
% 19.99/20.37 tc_Nat_Onat ) }.
% 19.99/20.37 (82740) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__semigroup__add(
% 19.99/20.37 tc_Nat_Onat ) }.
% 19.99/20.37 (82741) {G0,W2,D2,L1,V0,M1} { class_Rings_Oordered__semiring( tc_Nat_Onat
% 19.99/20.37 ) }.
% 19.99/20.37 (82742) {G0,W2,D2,L1,V0,M1} { class_Rings_Ono__zero__divisors( tc_Nat_Onat
% 19.99/20.37 ) }.
% 19.99/20.37 (82743) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocomm__monoid__add( tc_Nat_Onat
% 19.99/20.37 ) }.
% 19.99/20.37 (82744) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__1( tc_Nat_Onat
% 19.99/20.37 ) }.
% 19.99/20.37 (82745) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__0( tc_Nat_Onat
% 19.99/20.37 ) }.
% 19.99/20.37 (82746) {G0,W2,D2,L1,V0,M1} { class_Divides_Osemiring__div( tc_Nat_Onat )
% 19.99/20.37 }.
% 19.99/20.37 (82747) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring( tc_Nat_Onat )
% 19.99/20.37 }.
% 19.99/20.37 (82748) {G0,W2,D2,L1,V0,M1} { class_Rings_Ozero__neq__one( tc_Nat_Onat )
% 19.99/20.37 }.
% 19.99/20.37 (82749) {G0,W2,D2,L1,V0,M1} { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 19.99/20.37 (82750) {G0,W2,D2,L1,V0,M1} { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 19.99/20.37 (82751) {G0,W2,D2,L1,V0,M1} { class_Groups_Omonoid__mult( tc_Nat_Onat )
% 19.99/20.37 }.
% 19.99/20.37 (82752) {G0,W2,D2,L1,V0,M1} { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 19.99/20.37 (82753) {G0,W2,D2,L1,V0,M1} { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 19.99/20.37 (82754) {G0,W2,D2,L1,V0,M1} { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 19.99/20.37 (82755) {G0,W2,D2,L1,V0,M1} { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 19.99/20.37 (82756) {G0,W2,D2,L1,V0,M1} { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 19.99/20.37 (82757) {G0,W2,D2,L1,V0,M1} { class_Orderings_Oord( tc_Nat_Onat ) }.
% 19.99/20.37 (82758) {G0,W2,D2,L1,V0,M1} { class_Groups_Ominus( tc_Nat_Onat ) }.
% 19.99/20.37 (82759) {G0,W2,D2,L1,V0,M1} { class_Power_Opower( tc_Nat_Onat ) }.
% 19.99/20.37 (82760) {G0,W2,D2,L1,V0,M1} { class_Groups_Ozero( tc_Nat_Onat ) }.
% 19.99/20.37 (82761) {G0,W2,D2,L1,V0,M1} { class_Groups_Oone( tc_Nat_Onat ) }.
% 19.99/20.37 (82762) {G0,W2,D2,L1,V0,M1} { class_Rings_Odvd( tc_Nat_Onat ) }.
% 19.99/20.37 (82763) {G0,W2,D2,L1,V0,M1} { class_Lattices_Oboolean__algebra(
% 19.99/20.37 tc_HOL_Obool ) }.
% 19.99/20.37 (82764) {G0,W2,D2,L1,V0,M1} { class_Orderings_Opreorder( tc_HOL_Obool )
% 19.99/20.37 }.
% 19.99/20.37 (82765) {G0,W2,D2,L1,V0,M1} { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 19.99/20.37 (82766) {G0,W2,D2,L1,V0,M1} { class_Orderings_Oord( tc_HOL_Obool ) }.
% 19.99/20.37 (82767) {G0,W2,D2,L1,V0,M1} { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 19.99/20.37 (82768) {G0,W2,D2,L1,V0,M1} { class_Groups_Ominus( tc_HOL_Obool ) }.
% 19.99/20.37 (82769) {G0,W2,D2,L1,V0,M1} {
% 19.99/20.37 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82770) {G0,W2,D2,L1,V0,M1} { class_Rings_Odivision__ring__inverse__zero(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82771) {G0,W2,D2,L1,V0,M1} { class_RealVector_Oreal__normed__algebra(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82772) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__ab__semigroup__add(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82773) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__1__no__zero__divisors(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82774) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__no__zero__divisors(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82775) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocancel__semigroup__add(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82776) {G0,W2,D2,L1,V0,M1} { class_Fields_Ofield__inverse__zero(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82777) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__semigroup__mult(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82778) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocomm__monoid__mult(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82779) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__semigroup__add(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82780) {G0,W2,D2,L1,V0,M1} { class_Rings_Ono__zero__divisors(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82781) {G0,W2,D2,L1,V0,M1} { class_Groups_Ocomm__monoid__add(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82782) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__1(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82783) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring__0(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82784) {G0,W2,D2,L1,V0,M1} { class_Rings_Odivision__ring(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82785) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__semiring(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82786) {G0,W2,D2,L1,V0,M1} { class_Groups_Oab__group__add(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82787) {G0,W2,D2,L1,V0,M1} { class_Rings_Ozero__neq__one(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82788) {G0,W2,D2,L1,V0,M1} { class_Groups_Omonoid__mult(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82789) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__ring__1(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82790) {G0,W2,D2,L1,V0,M1} { class_Groups_Omonoid__add(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82791) {G0,W2,D2,L1,V0,M1} { class_Rings_Osemiring__0(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82792) {G0,W2,D2,L1,V0,M1} { class_Groups_Ogroup__add(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82793) {G0,W2,D2,L1,V0,M1} { class_Rings_Omult__zero( tc_Complex_Ocomplex
% 19.99/20.37 ) }.
% 19.99/20.37 (82794) {G0,W2,D2,L1,V0,M1} { class_Rings_Ocomm__ring( tc_Complex_Ocomplex
% 19.99/20.37 ) }.
% 19.99/20.37 (82795) {G0,W2,D2,L1,V0,M1} { class_Int_Oring__char__0(
% 19.99/20.37 tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82796) {G0,W2,D2,L1,V0,M1} { class_Rings_Osemiring( tc_Complex_Ocomplex )
% 19.99/20.37 }.
% 19.99/20.37 (82797) {G0,W2,D2,L1,V0,M1} { class_Groups_Ouminus( tc_Complex_Ocomplex )
% 19.99/20.37 }.
% 19.99/20.37 (82798) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring__1( tc_Complex_Ocomplex )
% 19.99/20.37 }.
% 19.99/20.37 (82799) {G0,W2,D2,L1,V0,M1} { class_Groups_Ominus( tc_Complex_Ocomplex )
% 19.99/20.37 }.
% 19.99/20.37 (82800) {G0,W2,D2,L1,V0,M1} { class_Fields_Ofield( tc_Complex_Ocomplex )
% 19.99/20.37 }.
% 19.99/20.37 (82801) {G0,W2,D2,L1,V0,M1} { class_Power_Opower( tc_Complex_Ocomplex )
% 19.99/20.37 }.
% 19.99/20.37 (82802) {G0,W2,D2,L1,V0,M1} { class_Groups_Ozero( tc_Complex_Ocomplex )
% 19.99/20.37 }.
% 19.99/20.37 (82803) {G0,W2,D2,L1,V0,M1} { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82804) {G0,W2,D2,L1,V0,M1} { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82805) {G0,W2,D2,L1,V0,M1} { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82806) {G0,W2,D2,L1,V0,M1} { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 19.99/20.37 (82807) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Oidom( X ),
% 19.99/20.37 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 19.99/20.37 tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82808) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 19.99/20.37 ) ) }.
% 19.99/20.37 (82809) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 19.99/20.37 X ) ) }.
% 19.99/20.37 (82810) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 19.99/20.37 ) }.
% 19.99/20.37 (82811) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 19.99/20.37 }.
% 19.99/20.37 (82812) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82813) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82814) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82815) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82816) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Ocancel__comm__monoid__add( X
% 19.99/20.37 ), class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) )
% 19.99/20.37 }.
% 19.99/20.37 (82817) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Oidom( X ),
% 19.99/20.37 class_Rings_Oring__1__no__zero__divisors( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82818) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82819) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82820) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Oidom( X ),
% 19.99/20.37 class_Rings_Oring__no__zero__divisors( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82821) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82822) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82823) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82824) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Ocancel__comm__monoid__add( X
% 19.99/20.37 ), class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82825) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Rings_Olinordered__semiring( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82826) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Rings_Olinordered__semidom( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82827) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.37 class_Groups_Oab__semigroup__mult( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82828) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.37 class_Groups_Ocomm__monoid__mult( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82829) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 19.99/20.37 class_Groups_Oab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82830) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Rings_Oordered__semiring( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82831) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Oidom( X ),
% 19.99/20.37 class_Rings_Ono__zero__divisors( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82832) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 19.99/20.37 class_Groups_Ocomm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82833) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Rings_Olinordered__ring( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82834) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Rings_Olinordered__idom( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82835) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.37 class_Rings_Ocomm__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82836) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.37 class_Rings_Ocomm__semiring__0( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82837) {G0,W5,D3,L2,V1,M2} { ! class_Fields_Ofield( X ),
% 19.99/20.37 class_Divides_Osemiring__div( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82838) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.37 class_Rings_Ocomm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82839) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Oab__group__add( X ),
% 19.99/20.37 class_Groups_Oab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82840) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.37 class_Rings_Ozero__neq__one( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82841) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Rings_Oordered__ring( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82842) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Orderings_Opreorder( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82843) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Orderings_Olinorder( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82844) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.37 class_Groups_Omonoid__mult( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82845) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__ring__1( X ),
% 19.99/20.37 class_Rings_Ocomm__ring__1( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82846) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Ocomm__monoid__add( X ),
% 19.99/20.37 class_Groups_Omonoid__add( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82847) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.37 class_Rings_Osemiring__0( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82848) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Oab__group__add( X ),
% 19.99/20.37 class_Groups_Ogroup__add( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82849) {G0,W5,D3,L2,V1,M2} { ! class_Fields_Ofield( X ),
% 19.99/20.37 class_Divides_Oring__div( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82850) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.37 class_Rings_Omult__zero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82851) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__ring( X ),
% 19.99/20.37 class_Rings_Ocomm__ring( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82852) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Orderings_Oorder( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82853) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Int_Oring__char__0( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82854) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__0( X ),
% 19.99/20.37 class_Rings_Osemiring( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82855) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Olinordered__idom( X ),
% 19.99/20.37 class_Orderings_Oord( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82856) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Oab__group__add( X ),
% 19.99/20.37 class_Groups_Ouminus( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82857) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__ring__1( X ),
% 19.99/20.37 class_Rings_Oring__1( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82858) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Oab__group__add( X ),
% 19.99/20.37 class_Groups_Ominus( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82859) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.37 class_Power_Opower( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82860) {G0,W5,D3,L2,V1,M2} { ! class_Groups_Ozero( X ),
% 19.99/20.37 class_Groups_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82861) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__ring( X ),
% 19.99/20.37 class_Rings_Oring( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82862) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Oidom( X ), class_Rings_Oidom
% 19.99/20.37 ( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82863) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.37 class_Groups_Oone( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.37 (82864) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Ocomm__semiring__1( X ),
% 19.99/20.38 class_Rings_Odvd( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.38 (82865) {G0,W7,D3,L2,V2,M2} { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 19.99/20.38 (82866) {G0,W7,D3,L2,V2,M2} { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 19.99/20.38 (82867) {G0,W5,D4,L1,V0,M1} { v_s____ = c_Groups_Ozero__class_Ozero(
% 19.99/20.38 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) }.
% 19.99/20.38
% 19.99/20.38
% 19.99/20.38 Total Proof:
% 19.99/20.38
% 19.99/20.38 eqswap: (82871) {G0,W5,D4,L1,V0,M1} { ! c_Groups_Ozero__class_Ozero(
% 19.99/20.38 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) = v_pa____ }.
% 19.99/20.38 parent0[0]: (81247) {G0,W5,D4,L1,V0,M1} { ! v_pa____ =
% 19.99/20.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 19.99/20.38 }.
% 19.99/20.38 substitution0:
% 19.99/20.38 end
% 19.99/20.38
% 19.99/20.38 subsumption: (1) {G0,W5,D4,L1,V0,M1} I { ! c_Groups_Ozero__class_Ozero(
% 19.99/20.38 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) ==> v_pa____ }.
% 19.99/20.38 parent0: (82871) {G0,W5,D4,L1,V0,M1} { ! c_Groups_Ozero__class_Ozero(
% 19.99/20.38 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) = v_pa____ }.
% 19.99/20.38 substitution0:
% 19.99/20.38 end
% 19.99/20.38 permutation0:
% 19.99/20.38 0 ==> 0
% 19.99/20.38 end
% 19.99/20.38
% 19.99/20.38 eqswap: (83061) {G0,W29,D10,L1,V0,M1} { hAPP( hAPP(
% 19.99/20.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.38 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 19.99/20.38 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 19.99/20.38 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 19.99/20.38 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 19.99/20.38 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 19.99/20.38 tc_Complex_Ocomplex ) ) ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex,
% 19.99/20.38 v_a____, v_pa____ ) ) ), v_s____ ) = v_pa____ }.
% 19.99/20.38 parent0[0]: (81338) {G0,W29,D10,L1,V0,M1} { v_pa____ = hAPP( hAPP(
% 19.99/20.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.38 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 19.99/20.38 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 19.99/20.38 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 19.99/20.38 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 19.99/20.38 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 19.99/20.38 tc_Complex_Ocomplex ) ) ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex,
% 19.99/20.38 v_a____, v_pa____ ) ) ), v_s____ ) }.
% 19.99/20.38 substitution0:
% 19.99/20.38 end
% 19.99/20.38
% 19.99/20.38 subsumption: (84) {G0,W29,D10,L1,V0,M1} I { hAPP( hAPP(
% 19.99/20.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.38 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 19.99/20.38 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 19.99/20.38 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 19.99/20.38 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 19.99/20.38 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 19.99/20.38 tc_Complex_Ocomplex ) ) ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex,
% 19.99/20.38 v_a____, v_pa____ ) ) ), v_s____ ) ==> v_pa____ }.
% 19.99/20.38 parent0: (83061) {G0,W29,D10,L1,V0,M1} { hAPP( hAPP(
% 19.99/20.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.38 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 19.99/20.38 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 19.99/20.38 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 19.99/20.38 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 19.99/20.38 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 19.99/20.38 tc_Complex_Ocomplex ) ) ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex,
% 19.99/20.38 v_a____, v_pa____ ) ) ), v_s____ ) = v_pa____ }.
% 19.99/20.38 substitution0:
% 19.99/20.38 end
% 19.99/20.38 permutation0:
% 19.99/20.38 0 ==> 0
% 19.99/20.38 end
% 19.99/20.38
% 19.99/20.38 subsumption: (232) {G0,W15,D5,L3,V3,M3} I { !
% 19.99/20.38 class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 19.99/20.38 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 19.99/20.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ==>
% 19.99/20.38 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.38 parent0: (81505) {G0,W15,D5,L3,V3,M3} { !
% 19.99/20.38 class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 19.99/20.38 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 19.99/20.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 19.99/20.38 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.38 substitution0:
% 19.99/20.38 X := X
% 19.99/20.38 Y := Y
% 19.99/20.38 Z := Z
% 19.99/20.38 end
% 19.99/20.38 permutation0:
% 19.99/20.38 0 ==> 0
% 19.99/20.38 1 ==> 1
% 19.99/20.38 2 ==> 2
% 19.99/20.38 end
% 19.99/20.38
% 19.99/20.38 subsumption: (1321) {G0,W2,D2,L1,V0,M1} I { class_Rings_Oidom(
% 19.99/20.40 tc_Complex_Ocomplex ) }.
% 19.99/20.40 parent0: (82804) {G0,W2,D2,L1,V0,M1} { class_Rings_Oidom(
% 19.99/20.40 tc_Complex_Ocomplex ) }.
% 19.99/20.40 substitution0:
% 19.99/20.40 end
% 19.99/20.40 permutation0:
% 19.99/20.40 0 ==> 0
% 19.99/20.40 end
% 19.99/20.40
% 19.99/20.40 subsumption: (1337) {G0,W5,D3,L2,V1,M2} I { ! class_Rings_Oidom( X ),
% 19.99/20.40 class_Rings_Oring__no__zero__divisors( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.40 parent0: (82820) {G0,W5,D3,L2,V1,M2} { ! class_Rings_Oidom( X ),
% 19.99/20.40 class_Rings_Oring__no__zero__divisors( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.40 substitution0:
% 19.99/20.40 X := X
% 19.99/20.40 end
% 19.99/20.40 permutation0:
% 19.99/20.40 0 ==> 0
% 19.99/20.40 1 ==> 1
% 19.99/20.40 end
% 19.99/20.40
% 19.99/20.40 eqswap: (88695) {G0,W5,D4,L1,V0,M1} { c_Groups_Ozero__class_Ozero(
% 19.99/20.40 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) = v_s____ }.
% 19.99/20.40 parent0[0]: (82867) {G0,W5,D4,L1,V0,M1} { v_s____ =
% 19.99/20.40 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 19.99/20.40 }.
% 19.99/20.40 substitution0:
% 19.99/20.40 end
% 19.99/20.40
% 19.99/20.40 subsumption: (1384) {G0,W5,D4,L1,V0,M1} I { c_Groups_Ozero__class_Ozero(
% 19.99/20.40 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) ==> v_s____ }.
% 19.99/20.40 parent0: (88695) {G0,W5,D4,L1,V0,M1} { c_Groups_Ozero__class_Ozero(
% 19.99/20.40 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) = v_s____ }.
% 19.99/20.40 substitution0:
% 19.99/20.40 end
% 19.99/20.40 permutation0:
% 19.99/20.40 0 ==> 0
% 19.99/20.40 end
% 19.99/20.40
% 19.99/20.40 paramod: (88698) {G1,W3,D2,L1,V0,M1} { ! v_s____ ==> v_pa____ }.
% 19.99/20.40 parent0[0]: (1384) {G0,W5,D4,L1,V0,M1} I { c_Groups_Ozero__class_Ozero(
% 19.99/20.40 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) ==> v_s____ }.
% 19.99/20.40 parent1[0; 2]: (1) {G0,W5,D4,L1,V0,M1} I { ! c_Groups_Ozero__class_Ozero(
% 19.99/20.40 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) ==> v_pa____ }.
% 19.99/20.40 substitution0:
% 19.99/20.40 end
% 19.99/20.40 substitution1:
% 19.99/20.40 end
% 19.99/20.40
% 19.99/20.40 subsumption: (1691) {G1,W3,D2,L1,V0,M1} S(1);d(1384) { ! v_s____ ==>
% 19.99/20.40 v_pa____ }.
% 19.99/20.40 parent0: (88698) {G1,W3,D2,L1,V0,M1} { ! v_s____ ==> v_pa____ }.
% 19.99/20.40 substitution0:
% 19.99/20.40 end
% 19.99/20.40 permutation0:
% 19.99/20.40 0 ==> 0
% 19.99/20.40 end
% 19.99/20.40
% 19.99/20.40 paramod: (88702) {G1,W27,D9,L1,V0,M1} { hAPP( hAPP(
% 19.99/20.40 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.40 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 19.99/20.40 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 19.99/20.40 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 19.99/20.40 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 19.99/20.40 tc_Complex_Ocomplex ), v_s____ ) ) ), c_Polynomial_Oorder(
% 19.99/20.40 tc_Complex_Ocomplex, v_a____, v_pa____ ) ) ), v_s____ ) ==> v_pa____ }.
% 19.99/20.40 parent0[0]: (1384) {G0,W5,D4,L1,V0,M1} I { c_Groups_Ozero__class_Ozero(
% 19.99/20.40 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) ==> v_s____ }.
% 19.99/20.40 parent1[0; 20]: (84) {G0,W29,D10,L1,V0,M1} I { hAPP( hAPP(
% 19.99/20.40 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.40 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 19.99/20.40 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 19.99/20.40 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 19.99/20.40 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 19.99/20.40 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 19.99/20.40 tc_Complex_Ocomplex ) ) ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex,
% 19.99/20.40 v_a____, v_pa____ ) ) ), v_s____ ) ==> v_pa____ }.
% 19.99/20.40 substitution0:
% 19.99/20.40 end
% 19.99/20.40 substitution1:
% 19.99/20.40 end
% 19.99/20.40
% 19.99/20.40 subsumption: (20175) {G1,W27,D9,L1,V0,M1} S(84);d(1384) { hAPP( hAPP(
% 19.99/20.40 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.40 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 19.99/20.40 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 19.99/20.40 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 19.99/20.40 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 19.99/20.40 tc_Complex_Ocomplex ), v_s____ ) ) ), c_Polynomial_Oorder(
% 19.99/20.40 tc_Complex_Ocomplex, v_a____, v_pa____ ) ) ), v_s____ ) ==> v_pa____ }.
% 19.99/20.40 parent0: (88702) {G1,W27,D9,L1,V0,M1} { hAPP( hAPP(
% 19.99/20.40 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.40 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 19.99/20.40 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 19.99/20.40 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 19.99/20.40 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 19.99/20.40 tc_Complex_Ocomplex ), v_s____ ) ) ), c_Polynomial_Oorder(
% 19.99/20.40 tc_Complex_Ocomplex, v_a____, v_pa____ ) ) ), v_s____ ) ==> v_pa____ }.
% 19.99/20.40 substitution0:
% 19.99/20.40 end
% 19.99/20.40 permutation0:
% 19.99/20.40 0 ==> 0
% 19.99/20.40 end
% 19.99/20.40
% 19.99/20.40 resolution: (88704) {G1,W3,D3,L1,V0,M1} {
% 19.99/20.40 class_Rings_Oring__no__zero__divisors( tc_Polynomial_Opoly(
% 19.99/20.40 tc_Complex_Ocomplex ) ) }.
% 19.99/20.40 parent0[0]: (1337) {G0,W5,D3,L2,V1,M2} I { ! class_Rings_Oidom( X ),
% 19.99/20.40 class_Rings_Oring__no__zero__divisors( tc_Polynomial_Opoly( X ) ) }.
% 19.99/20.40 parent1[0]: (1321) {G0,W2,D2,L1,V0,M1} I { class_Rings_Oidom(
% 19.99/20.40 tc_Complex_Ocomplex ) }.
% 19.99/20.40 substitution0:
% 19.99/20.40 X := tc_Complex_Ocomplex
% 19.99/20.40 end
% 19.99/20.40 substitution1:
% 19.99/20.40 end
% 19.99/20.40
% 19.99/20.40 subsumption: (29050) {G1,W3,D3,L1,V0,M1} R(1337,1321) {
% 19.99/20.40 class_Rings_Oring__no__zero__divisors( tc_Polynomial_Opoly(
% 19.99/20.40 tc_Complex_Ocomplex ) ) }.
% 19.99/20.40 parent0: (88704) {G1,W3,D3,L1,V0,M1} {
% 19.99/20.40 class_Rings_Oring__no__zero__divisors( tc_Polynomial_Opoly(
% 19.99/20.40 tc_Complex_Ocomplex ) ) }.
% 19.99/20.40 substitution0:
% 19.99/20.40 end
% 19.99/20.40 permutation0:
% 19.99/20.40 0 ==> 0
% 19.99/20.40 end
% 19.99/20.40
% 19.99/20.40 eqswap: (88705) {G0,W15,D5,L3,V3,M3} { ! c_Groups_Ozero__class_Ozero( Y )
% 19.99/20.40 = X, ! class_Rings_Oring__no__zero__divisors( Y ), hAPP( hAPP(
% 19.99/20.40 c_Groups_Otimes__class_Otimes( Y ), Z ), X ) ==>
% 19.99/20.40 c_Groups_Ozero__class_Ozero( Y ) }.
% 19.99/20.40 parent0[1]: (232) {G0,W15,D5,L3,V3,M3} I { !
% 19.99/20.40 class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 19.99/20.40 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 19.99/20.40 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ==>
% 19.99/20.40 c_Groups_Ozero__class_Ozero( X ) }.
% 19.99/20.40 substitution0:
% 19.99/20.40 X := Y
% 19.99/20.40 Y := X
% 19.99/20.40 Z := Z
% 19.99/20.40 end
% 19.99/20.40
% 19.99/20.40 resolution: (88710) {G1,W16,D6,L2,V2,M2} { ! c_Groups_Ozero__class_Ozero(
% 19.99/20.40 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) = X, hAPP( hAPP(
% 19.99/20.40 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.40 ), Y ), X ) ==> c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 19.99/20.40 tc_Complex_Ocomplex ) ) }.
% 19.99/20.40 parent0[1]: (88705) {G0,W15,D5,L3,V3,M3} { ! c_Groups_Ozero__class_Ozero(
% 19.99/20.40 Y ) = X, ! class_Rings_Oring__no__zero__divisors( Y ), hAPP( hAPP(
% 19.99/20.40 c_Groups_Otimes__class_Otimes( Y ), Z ), X ) ==>
% 19.99/20.40 c_Groups_Ozero__class_Ozero( Y ) }.
% 19.99/20.40 parent1[0]: (29050) {G1,W3,D3,L1,V0,M1} R(1337,1321) {
% 19.99/20.40 class_Rings_Oring__no__zero__divisors( tc_Polynomial_Opoly(
% 19.99/20.40 tc_Complex_Ocomplex ) ) }.
% 19.99/20.40 substitution0:
% 19.99/20.40 X := X
% 19.99/20.40 Y := tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.40 Z := Y
% 19.99/20.40 end
% 19.99/20.40 substitution1:
% 19.99/20.40 end
% 19.99/20.40
% 19.99/20.40 paramod: (88712) {G1,W14,D6,L2,V2,M2} { hAPP( hAPP(
% 19.99/20.40 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.40 ), X ), Y ) ==> v_s____, ! c_Groups_Ozero__class_Ozero(
% 19.99/20.40 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) = Y }.
% 19.99/20.40 parent0[0]: (1384) {G0,W5,D4,L1,V0,M1} I { c_Groups_Ozero__class_Ozero(
% 19.99/20.40 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) ==> v_s____ }.
% 19.99/20.40 parent1[1; 8]: (88710) {G1,W16,D6,L2,V2,M2} { !
% 19.99/20.40 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 19.99/20.40 = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly(
% 19.99/20.40 tc_Complex_Ocomplex ) ), Y ), X ) ==> c_Groups_Ozero__class_Ozero(
% 19.99/20.40 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) }.
% 19.99/20.40 substitution0:
% 19.99/20.40 end
% 19.99/20.40 substitution1:
% 19.99/20.40 X := Y
% 19.99/20.40 Y := X
% 19.99/20.40 end
% 19.99/20.40
% 19.99/20.40 paramod: (88714) {G1,W12,D6,L2,V2,M2} { ! v_s____ = X, hAPP( hAPP(
% 19.99/20.40 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.40 ), Y ), X ) ==> v_s____ }.
% 19.99/20.40 parent0[0]: (1384) {G0,W5,D4,L1,V0,M1} I { c_Groups_Ozero__class_Ozero(
% 19.99/20.40 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) ==> v_s____ }.
% 19.99/20.40 parent1[1; 2]: (88712) {G1,W14,D6,L2,V2,M2} { hAPP( hAPP(
% 19.99/20.40 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.40 ), X ), Y ) ==> v_s____, ! c_Groups_Ozero__class_Ozero(
% 19.99/20.40 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) = Y }.
% 19.99/20.40 substitution0:
% 19.99/20.40 end
% 19.99/20.40 substitution1:
% 19.99/20.40 X := Y
% 19.99/20.40 Y := X
% 19.99/20.40 end
% 19.99/20.40
% 19.99/20.40 eqswap: (88715) {G1,W12,D6,L2,V2,M2} { ! X = v_s____, hAPP( hAPP(
% 19.99/20.40 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.40 ), Y ), X ) ==> v_s____ }.
% 19.99/20.40 parent0[0]: (88714) {G1,W12,D6,L2,V2,M2} { ! v_s____ = X, hAPP( hAPP(
% 19.99/20.40 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.40 ), Y ), X ) ==> v_s____ }.
% 19.99/20.40 substitution0:
% 19.99/20.40 X := X
% 19.99/20.40 Y := Y
% 19.99/20.40 end
% 19.99/20.40
% 19.99/20.40 subsumption: (80322) {G2,W12,D6,L2,V2,M2} R(232,29050);d(1384);d(1384) { !
% 19.99/20.40 X = v_s____, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.40 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), Y ), X ) ==> v_s____ }.
% 19.99/20.40 parent0: (88715) {G1,W12,D6,L2,V2,M2} { ! X = v_s____, hAPP( hAPP(
% 19.99/20.40 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.40 ), Y ), X ) ==> v_s____ }.
% 19.99/20.40 substitution0:
% 19.99/20.40 X := X
% 19.99/20.40 Y := Y
% 19.99/20.40 end
% 19.99/20.40 permutation0:
% 19.99/20.40 0 ==> 0
% 19.99/20.40 1 ==> 1
% 19.99/20.40 end
% 19.99/20.40
% 19.99/20.40 eqswap: (88718) {G2,W12,D6,L2,V2,M2} { ! v_s____ = X, hAPP( hAPP(
% 19.99/20.40 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.40 ), Y ), X ) ==> v_s____ }.
% 19.99/20.40 parent0[0]: (80322) {G2,W12,D6,L2,V2,M2} R(232,29050);d(1384);d(1384) { ! X
% 19.99/20.40 = v_s____, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 19.99/20.40 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), Y ), X ) ==> v_s____ }.
% 19.99/20.40 substitution0:
% 19.99/20.40 X := X
% 19.99/20.40 Y := Y
% 19.99/20.40 end
% 19.99/20.40
% 19.99/20.40 eqrefl: (88721) {G0,W9,D6,L1,V1,M1} { hAPP( hAPP(
% 19.99/20.40 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.40 ), X ), v_s____ ) ==> v_s____ }.
% 19.99/20.40 parent0[0]: (88718) {G2,W12,D6,L2,V2,M2} { ! v_s____ = X, hAPP( hAPP(
% 19.99/20.40 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.40 ), Y ), X ) ==> v_s____ }.
% 19.99/20.40 substitution0:
% 19.99/20.40 X := v_s____
% 19.99/20.40 Y := X
% 19.99/20.40 end
% 19.99/20.40
% 19.99/20.40 subsumption: (80594) {G3,W9,D6,L1,V1,M1} Q(80322) { hAPP( hAPP(
% 19.99/20.40 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.40 ), X ), v_s____ ) ==> v_s____ }.
% 19.99/20.40 parent0: (88721) {G0,W9,D6,L1,V1,M1} { hAPP( hAPP(
% 19.99/20.40 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.40 ), X ), v_s____ ) ==> v_s____ }.
% 19.99/20.40 substitution0:
% 19.99/20.40 X := X
% 19.99/20.40 end
% 19.99/20.40 permutation0:
% 19.99/20.40 0 ==> 0
% 19.99/20.40 end
% 19.99/20.40
% 19.99/20.40 paramod: (88726) {G2,W3,D2,L1,V0,M1} { v_s____ ==> v_pa____ }.
% 19.99/20.40 parent0[0]: (80594) {G3,W9,D6,L1,V1,M1} Q(80322) { hAPP( hAPP(
% 19.99/20.40 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.40 ), X ), v_s____ ) ==> v_s____ }.
% 19.99/20.40 parent1[0; 1]: (20175) {G1,W27,D9,L1,V0,M1} S(84);d(1384) { hAPP( hAPP(
% 19.99/20.40 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 19.99/20.40 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 19.99/20.40 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 19.99/20.40 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 19.99/20.40 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 19.99/20.40 tc_Complex_Ocomplex ), v_s____ ) ) ), c_Polynomial_Oorder(
% 19.99/20.40 tc_Complex_Ocomplex, v_a____, v_pa____ ) ) ), v_s____ ) ==> v_pa____ }.
% 19.99/20.40 substitution0:
% 19.99/20.40 X := hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 19.99/20.40 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 19.99/20.40 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 19.99/20.40 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 19.99/20.40 tc_Complex_Ocomplex ), v_s____ ) ) ), c_Polynomial_Oorder(
% 19.99/20.40 tc_Complex_Ocomplex, v_a____, v_pa____ ) )
% 19.99/20.40 end
% 19.99/20.40 substitution1:
% 19.99/20.40 end
% 19.99/20.40
% 19.99/20.40 resolution: (88727) {G2,W0,D0,L0,V0,M0} { }.
% 19.99/20.40 parent0[0]: (1691) {G1,W3,D2,L1,V0,M1} S(1);d(1384) { ! v_s____ ==>
% 19.99/20.40 v_pa____ }.
% 19.99/20.40 parent1[0]: (88726) {G2,W3,D2,L1,V0,M1} { v_s____ ==> v_pa____ }.
% 19.99/20.40 substitution0:
% 19.99/20.40 end
% 19.99/20.40 substitution1:
% 19.99/20.40 end
% 19.99/20.40
% 19.99/20.40 subsumption: (81244) {G4,W0,D0,L0,V0,M0} S(20175);d(80594);r(1691) { }.
% 19.99/20.40 parent0: (88727) {G2,W0,D0,L0,V0,M0} { }.
% 19.99/20.40 substitution0:
% 19.99/20.40 end
% 19.99/20.40 permutation0:
% 19.99/20.40 end
% 19.99/20.40
% 19.99/20.40 Proof check complete!
% 19.99/20.40
% 19.99/20.40 Memory use:
% 19.99/20.40
% 19.99/20.40 space for terms: 2487261
% 19.99/20.40 space for clauses: 3555152
% 19.99/20.40
% 19.99/20.40
% 19.99/20.40 clauses generated: 294861
% 19.99/20.40 clauses kept: 81245
% 19.99/20.40 clauses selected: 1137
% 19.99/20.40 clauses deleted: 552
% 19.99/20.40 clauses inuse deleted: 1
% 19.99/20.40
% 19.99/20.40 subsentry: 1693269
% 19.99/20.40 literals s-matched: 765592
% 19.99/20.40 literals matched: 728881
% 19.99/20.40 full subsumption: 533001
% 19.99/20.40
% 19.99/20.40 checksum: -849941115
% 19.99/20.40
% 19.99/20.40
% 19.99/20.40 Bliksem ended
%------------------------------------------------------------------------------