TSTP Solution File: SWW285+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW285+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 23:21:50 EDT 2022
% Result : Timeout 300.07s 300.49s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW285+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % 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 : Sun Jun 5 11:35:37 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.98/1.66 *** allocated 10000 integers for termspace/termends
% 0.98/1.66 *** allocated 10000 integers for clauses
% 0.98/1.66 *** allocated 10000 integers for justifications
% 0.98/1.66 *** allocated 15000 integers for termspace/termends
% 0.98/1.66 *** allocated 22500 integers for termspace/termends
% 0.98/1.66 *** allocated 33750 integers for termspace/termends
% 0.98/1.66 Bliksem 1.12
% 0.98/1.66
% 0.98/1.66
% 0.98/1.66 Automatic Strategy Selection
% 0.98/1.66
% 0.98/1.66 *** allocated 50625 integers for termspace/termends
% 0.98/1.66 *** allocated 75937 integers for termspace/termends
% 0.98/1.66 *** allocated 113905 integers for termspace/termends
% 0.98/1.66
% 0.98/1.66 Clauses:
% 0.98/1.66
% 0.98/1.66 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.98/1.66 { v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.98/1.66 tc_Complex_Ocomplex ) ) }.
% 0.98/1.66 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 0.98/1.66 X, T ) = hAPP( X, U ) }.
% 0.98/1.66 { ! hAPP( X, skol2( X ) ) = hAPP( X, skol23( X ) ),
% 0.98/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.98/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), !
% 0.98/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 0.98/1.66 ( tc_Polynomial_Opoly( X ) ),
% 0.98/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.98/1.66 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.98/1.66 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), skol3 ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), v_q =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.98/1.66 }.
% 0.98/1.66 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q ), skol3 ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), v_q =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.98/1.66 }.
% 0.98/1.66 { ! v_q = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.98/1.66 tc_Complex_Ocomplex ) ), ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex
% 0.98/1.66 , v_p ), X ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.98/1.66 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q ), X ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.66 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.66 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.66 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.66 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.66 }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.98/1.66 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.98/1.66 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 0.98/1.66 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 0.98/1.66 c_Polynomial_Ocoeff( X, Y ) }.
% 0.98/1.66 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.98/1.66 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.98/1.66 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.98/1.66 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 0.98/1.66 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol4( X
% 0.98/1.66 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol4( X, Y, Z ) ), Z = Y
% 0.98/1.66 }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.98/1.66 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.66 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.66 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 0.98/1.66 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex, X ) ),
% 0.98/1.66 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol5( X ) ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.98/1.66 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.98/1.66 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha1( X
% 0.98/1.66 , Y, T ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha26( X
% 0.98/1.66 , Y, Z, T ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), ! alpha1( X, Y, T ), ! alpha26( X, Y, Z, T )
% 0.98/1.66 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 0.98/1.66 ( X, T, Z ), Y ) }.
% 0.98/1.66 { ! alpha26( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.98/1.66 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha26( X, Y, Z, T ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha26( X
% 0.98/1.66 , Y, Z, T ) }.
% 0.98/1.66 { ! alpha1( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { Z = c_Groups_Ozero__class_Ozero( X ), alpha1( X, Y, Z ) }.
% 0.98/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha1( X
% 0.98/1.66 , Y, Z ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.66 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.98/1.66 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.98/1.66 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.98/1.66 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.98/1.66 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), !
% 0.98/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ),
% 0.98/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.98/1.66 tc_Complex_Ocomplex ) ), v_q ), c_Polynomial_Odegree( tc_Complex_Ocomplex
% 0.98/1.66 , v_p ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.66 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), v_p ), v_r____ ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 0.98/1.66 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.66 , Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.98/1.66 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.98/1.66 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ), v_p
% 0.98/1.66 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.98/1.66 tc_Complex_Ocomplex ) ), v_q ), c_Polynomial_Odegree( tc_Complex_Ocomplex
% 0.98/1.66 , v_p ) ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.98/1.66 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.98/1.66 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 0.98/1.66 c_Polynomial_Odegree( X, Z ) ) }.
% 0.98/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 Y, T ), Z = Y }.
% 0.98/1.66 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 T, Y ), Z = Y }.
% 0.98/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 T, Y ), Z = Y }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.98/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.98/1.66 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.98/1.66 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.98/1.66 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.98/1.66 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.98/1.66 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.98/1.66 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.98/1.66 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 0.98/1.66 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.98/1.66 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.98/1.66 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.98/1.66 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.98/1.66 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.98/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 Y, Z ), T = Y }.
% 0.98/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 Y, Z ) }.
% 0.98/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 T, Y ), Z = Y }.
% 0.98/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 T, Y ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.98/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.98/1.66 ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.66 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.98/1.66 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.98/1.66 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.98/1.66 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.66 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.66 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 0.98/1.66 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.98/1.66 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.98/1.66 c_Polynomial_Odegree( X, Y ) ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), Y, Z ), Z = Y }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.98/1.66 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 0.98/1.66 Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.98/1.66 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.98/1.66 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.98/1.66 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.98/1.66 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 0.98/1.66 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.66 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.98/1.66 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.98/1.66 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.98/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.98/1.66 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.98/1.66 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.98/1.66 ) }.
% 0.98/1.66 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.98/1.66 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.98/1.66 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.98/1.66 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 0.98/1.66 .
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.98/1.66 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 0.98/1.66 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 0.98/1.66 .
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.98/1.66 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.98/1.66 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.98/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.66 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.98/1.66 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.66 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.66 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.66 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.66 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Nat_Onat ) ) = Z }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.98/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.98/1.66 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 0.98/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 0.98/1.66 c_Polynomial_OpCons( X, T,
% 0.98/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 0.98/1.66 .
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.98/1.66 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.98/1.66 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 0.98/1.66 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.98/1.66 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.98/1.66 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 0.98/1.66 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 0.98/1.66 .
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.98/1.66 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 0.98/1.66 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 0.98/1.66 ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.98/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) =
% 0.98/1.66 c_Polynomial_Odegree( X, Z ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.66 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.66 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.66 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.98/1.66 c_Polynomial_Odegree( X, Y ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 0.98/1.66 X, T, Z ), Y ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.98/1.66 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.98/1.66 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.66 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 0.98/1.66 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 0.98/1.66 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.98/1.66 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.98/1.66 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.98/1.66 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.98/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.98/1.66 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.66 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 0.98/1.66 ), Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.66 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.98/1.66 , Y ) ) }.
% 0.98/1.66 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.98/1.66 tc_Complex_Ocomplex ) ), v_q ), c_Polynomial_Odegree( tc_Complex_Ocomplex
% 0.98/1.66 , v_p ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.66 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), v_p ), skol6 ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.66 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.98/1.66 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.98/1.66 hAPP( Z, skol7( U, W, Z ) ) ) }.
% 0.98/1.66 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.98/1.66 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol7( X
% 0.98/1.66 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.98/1.66 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 0.98/1.66 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol24( X,
% 0.98/1.66 Y, Z ) ) ) ) }.
% 0.98/1.66 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.98/1.66 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.98/1.66 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.98/1.66 .
% 0.98/1.66 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.98/1.66 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.98/1.66 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Nat_Onat ) }.
% 0.98/1.66 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.98/1.66 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.98/1.66 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.98/1.66 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.98/1.66 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.98/1.66 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.98/1.66 }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.98/1.66 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.98/1.66 }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.98/1.66 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.98/1.66 }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.98/1.66 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.98/1.66 }.
% 0.98/1.66 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.66 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.98/1.66 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.98/1.66 ) }.
% 0.98/1.66 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.66 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.98/1.66 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.98/1.66 ) }.
% 0.98/1.66 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.66 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.66 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.66 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), skol8( Z, Y ) ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.98/1.66 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = T, T =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y, hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.98/1.66 ), X ), T ) ) }.
% 0.98/1.66 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol8( X, Y ) ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.98/1.66 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = Z, Z =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y, hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.98/1.66 ), X ), Z ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.66 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.66 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.98/1.66 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.66 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.98/1.66 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.66 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.66 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.98/1.66 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.98/1.66 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.98/1.66 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.98/1.66 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.66 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.66 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.98/1.66 Z, T ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.98/1.66 ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.98/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.98/1.66 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.66 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.66 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.66 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.66 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.66 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.66 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.66 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.66 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.66 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.98/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.66 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.66 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.98/1.66 ), U = Z, T = Y }.
% 0.98/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.66 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.66 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.98/1.66 ) }.
% 0.98/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.66 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.66 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.98/1.66 ) }.
% 0.98/1.66 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.98/1.66 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.66 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.98/1.66 ) ), T ), Y ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.98/1.66 ) ), Z ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.66 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.66 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.66 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.66 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.98/1.66 ) }.
% 0.98/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.66 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.66 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.98/1.66 ), ! U = T }.
% 0.98/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.66 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.66 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.98/1.66 ), ! Z = Y }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.98/1.66 ) }.
% 0.98/1.66 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.98/1.66 ( X ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.98/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.98/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.98/1.66 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.66 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.66 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 0.98/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.66 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.66 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Nat_Onat, Z, Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.66 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.66 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.98/1.66 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 0.98/1.66 }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.98/1.66 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 0.98/1.66 ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 0.98/1.66 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 0.98/1.66 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 0.98/1.66 , Y ) ) }.
% 0.98/1.66 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.98/1.66 ( tc_Nat_Onat ) ) = X }.
% 0.98/1.66 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Nat_Onat ), X ) = X }.
% 0.98/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.66 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.66 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.98/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.98/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.98/1.66 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.98/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.98/1.66 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.98/1.66 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.98/1.66 .
% 0.98/1.66 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.98/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.98/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.98/1.66 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.98/1.66 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.98/1.66 .
% 0.98/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.98/1.66 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.98/1.66 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.98/1.66 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.98/1.66 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.98/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.66 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.66 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.98/1.66 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.98/1.66 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.98/1.66 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.98/1.66 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.98/1.66 ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 0.98/1.66 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.66 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.66 }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 0.98/1.66 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.66 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.66 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.66 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.66 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.66 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.98/1.66 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.98/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.98/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.98/1.66 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.98/1.66 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.98/1.66 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.98/1.66 .
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Nat_Onat, Y, X ) }.
% 0.98/1.66 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.66 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.66 X ) ) }.
% 0.98/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.66 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.66 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.98/1.66 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.98/1.66 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 0.98/1.66 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 0.98/1.66 X, Z ), Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.98/1.66 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.98/1.66 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.98/1.66 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 0.98/1.66 ( X ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 0.98/1.66 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.98/1.66 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.98/1.66 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ),
% 0.98/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ),
% 0.98/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 0.98/1.66 c_Polynomial_Odegree( X, Y ) ) }.
% 0.98/1.66 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 0.98/1.66 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 0.98/1.66 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.66 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.98/1.66 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.66 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha2( X, Y ), Y = X }
% 0.98/1.66 .
% 0.98/1.66 { ! alpha2( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.66 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.66 { ! alpha2( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.66 { ! alpha2( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Nat_Onat, X, Y ), alpha2( X, Y ) }.
% 0.98/1.66 { ! alpha3( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.66 { ! alpha3( X, Y ), ! Y = X }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha3( X, Y ) }
% 0.98/1.66 .
% 0.98/1.66 { ! alpha3( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.66 { ! alpha3( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Nat_Onat, X, Y ), alpha3( X, Y ) }.
% 0.98/1.66 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.66 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.66 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Nat_Onat, Y, X ), Y = X }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.98/1.66 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Nat_Onat, Y, Z ) }.
% 0.98/1.66 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Nat_Onat, Y, Z ) }.
% 0.98/1.66 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 0.98/1.66 , Z ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 0.98/1.66 Z, Y ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Nat_Onat, Y, Z ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.66 { ! X = c_Nat_OSuc( X ) }.
% 0.98/1.66 { ! c_Nat_OSuc( X ) = X }.
% 0.98/1.66 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.98/1.66 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.98/1.66 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.98/1.66 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.66 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.98/1.66 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.66 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.98/1.66 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.66 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.98/1.66 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.98/1.66 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.98/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.98/1.66 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.98/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.98/1.66 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) ) }.
% 0.98/1.66 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.98/1.66 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.66 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.98/1.66 = Y }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.66 = Y }.
% 0.98/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.66 = Y }.
% 0.98/1.66 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.66 = Y }.
% 0.98/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.98/1.66 = Y }.
% 0.98/1.66 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.98/1.66 = Y }.
% 0.98/1.66 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.66 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.66 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.66 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.98/1.66 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.98/1.66 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.66 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.98/1.66 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.98/1.66 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.98/1.66 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.98/1.66 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.98/1.66 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.66 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.98/1.66 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.66 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.98/1.66 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.98/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.66 = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.98/1.66 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.66 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.98/1.66 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.66 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.66 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.98/1.66 tc_Nat_Onat ) ) = Y }.
% 0.98/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.98/1.66 tc_Nat_Onat ) ) = Y }.
% 0.98/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.98/1.66 tc_Nat_Onat ) }.
% 0.98/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.98/1.66 tc_Nat_Onat ) }.
% 0.98/1.66 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.98/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.98/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.98/1.66 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.98/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.66 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.98/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.66 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.98/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.98/1.66 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.98/1.66 , Y ), X ) }.
% 0.98/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 0.98/1.66 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 0.98/1.66 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 0.98/1.66 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.66 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.98/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.66 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.98/1.66 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.98/1.66 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.98/1.66 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.66 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.66 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.98/1.66 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.66 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.66 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.66 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.98/1.66 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha4( X, Y ), alpha27( X
% 0.98/1.66 , Y ) }.
% 0.98/1.66 { ! alpha4( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.66 { ! alpha27( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.66 { ! alpha27( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! alpha27( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Nat_Onat ) ) }.
% 0.98/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha27( X, Y ) }.
% 0.98/1.66 { ! alpha4( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Nat_Onat ) ) }.
% 0.98/1.66 { ! alpha4( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha4( X, Y ) }.
% 0.98/1.66 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha5( X, Y ), alpha28
% 0.98/1.66 ( X, Y ) }.
% 0.98/1.66 { ! alpha5( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.66 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.98/1.66 { ! alpha28( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.66 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.98/1.66 { ! alpha28( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! alpha28( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Nat_Onat ) ) }.
% 0.98/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha28( X, Y ) }.
% 0.98/1.66 { ! alpha5( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Nat_Onat ) ) }.
% 0.98/1.66 { ! alpha5( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha5( X, Y ) }.
% 0.98/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.98/1.66 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.98/1.66 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.66 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.98/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.66 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.98/1.66 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.98/1.66 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.98/1.66 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.98/1.66 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.66 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.98/1.66 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 0.98/1.66 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.66 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 0.98/1.66 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 0.98/1.66 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.66 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.66 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.66 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.98/1.66 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 0.98/1.66 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.66 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 0.98/1.66 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.66 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.98/1.66 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.98/1.66 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.98/1.66 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.66 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 0.98/1.66 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.66 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.98/1.66 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.98/1.66 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.98/1.66 Y ) ) ), Y ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.98/1.66 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.98/1.66 Y ) ) ), Y ) }.
% 0.98/1.66 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.98/1.66 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.98/1.66 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.98/1.66 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.98/1.66 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.66 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 0.98/1.66 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 0.98/1.66 ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Nat_Onat, Z, X ) }.
% 0.98/1.66 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Nat_Onat ) ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.98/1.66 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 0.98/1.66 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.66 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.98/1.66 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.98/1.66 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 0.98/1.66 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 0.98/1.66 ) ) }.
% 0.98/1.66 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Int_Oint, Y, X ) }.
% 0.98/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.98/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.98/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.98/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.98/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.98/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.98/1.66 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 0.98/1.66 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.98/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.98/1.66 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.98/1.66 , Z ), X ) ), T ) ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Int_Oint, U, T ) ) }.
% 0.98/1.66 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.98/1.66 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.98/1.66 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.98/1.66 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.98/1.66 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.98/1.66 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 0.98/1.66 ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.98/1.66 ) }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.66 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.98/1.66 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.66 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.66 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.66 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.66 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.98/1.66 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.98/1.66 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.66 = Y }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.66 ) }.
% 0.98/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.98/1.66 ( X ) }.
% 0.98/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.66 , Y ) }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.66 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.98/1.66 ) }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.98/1.66 ) }.
% 0.98/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.66 = Y }.
% 0.98/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.66 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.66 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.66 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.66 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.66 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.98/1.66 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.66 ( X, Y ) ) }.
% 0.98/1.66 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.98/1.66 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.66 ) ), Y ) }.
% 0.98/1.66 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.98/1.66 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.66 ( X, Y ) ) }.
% 0.98/1.66 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.98/1.66 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.98/1.66 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.98/1.66 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.98/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 Z, Y ) ) = Y }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.66 Y ) ) = Y }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.98/1.66 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.66 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.98/1.66 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.98/1.66 , Y ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.98/1.66 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.66 ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 0.98/1.66 , Z, Y ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.98/1.66 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 0.98/1.66 ) }.
% 0.98/1.66 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.98/1.66 c_Polynomial_Odegree( X, Y ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.98/1.66 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.98/1.66 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.66 Z ) = Y }.
% 0.98/1.66 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.66 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.98/1.66 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.98/1.66 ( X, Y ) }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 X ) }.
% 0.98/1.66 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.98/1.66 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.66 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.98/1.66 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.66 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.66 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.98/1.66 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.66 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.98/1.66 ) }.
% 0.98/1.66 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.98/1.66 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.66 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.66 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.98/1.66 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.98/1.66 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.98/1.66 ) ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Int_Oint, Z, X ) }.
% 0.98/1.66 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.98/1.66 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 0.98/1.66 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 0.98/1.66 ) }.
% 0.98/1.66 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.98/1.66 tc_Nat_Onat ), X ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.66 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.98/1.66 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 X ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 0.98/1.66 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.98/1.66 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.98/1.66 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.66 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.98/1.66 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 0.98/1.66 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.98/1.66 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.66 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.98/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.98/1.66 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.98/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.98/1.66 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.98/1.66 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.98/1.66 ( X, Z ) }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.66 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.66 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.98/1.66 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.66 }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.66 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.98/1.66 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.98/1.66 .
% 0.98/1.66 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.66 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.98/1.66 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.98/1.66 .
% 0.98/1.66 { ! class_Rings_Oidom( X ),
% 0.98/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( X, X,
% 0.98/1.66 c_Polynomial_Opoly( X, Y ) ), ! skol9( X, Z ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Rings_Oidom( X ),
% 0.98/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( X, X,
% 0.98/1.66 c_Polynomial_Opoly( X, Y ) ), alpha57( X, Y, skol9( X, Y ) ) }.
% 0.98/1.66 { ! alpha57( X, Y, Z ), ! skol10( T, U, W ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Nat_Onat ) }.
% 0.98/1.66 { ! alpha57( X, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.98/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, skol25( X, Y, Z ) )
% 0.98/1.66 , skol10( X, Y, Z ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 0.98/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) }.
% 0.98/1.66 { ! alpha57( X, Y, Z ), hAPP( c_Polynomial_Opoly( X, Y ), T ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, Y ),
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), T ), skol10( X, Y, Z ) ) ), hAPP(
% 0.98/1.66 c_Polynomial_Opoly( X, c_Polynomial_OpCons( X, Z, skol25( X, Y, Z ) ) ),
% 0.98/1.66 T ) ) ) }.
% 0.98/1.66 { T = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, U ), T
% 0.98/1.66 ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 0.98/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ), ! hAPP(
% 0.98/1.66 c_Polynomial_Opoly( X, Y ), skol28( X, Y, Z, T, U ) ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, Y ),
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), skol28( X, Y, Z, T, U ) ), T ) ), hAPP
% 0.98/1.66 ( c_Polynomial_Opoly( X, c_Polynomial_OpCons( X, Z, U ) ), skol28( X, Y,
% 0.98/1.66 Z, T, U ) ) ) ), alpha57( X, Y, Z ) }.
% 0.98/1.66 { c_Nat_Onat_Onat__size( c_Nat_OSuc( X ) ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Nat_Onat, c_Nat_Onat_Onat__size( X ), c_Nat_OSuc(
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.98/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.98/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.66 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.98/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.98/1.66 ( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.66 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Z ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.66 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Y ) }.
% 0.98/1.66 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.98/1.66 ( tc_Int_Oint ) }.
% 0.98/1.66 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.66 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.66 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.66 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 0.98/1.66 .
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.98/1.66 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.98/1.66 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.98/1.66 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.98/1.66 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.66 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.66 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 0.98/1.66 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.98/1.66 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.98/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.66 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.98/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.98/1.66 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.98/1.66 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.98/1.66 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.98/1.66 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 0.98/1.66 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 0.98/1.66 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.98/1.66 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 0.98/1.66 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.98/1.66 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.98/1.66 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.98/1.66 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.98/1.66 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.98/1.66 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.66 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.98/1.66 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.98/1.66 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.98/1.66 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.66 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.98/1.66 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 0.98/1.66 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.98/1.66 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.98/1.66 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.98/1.66 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.98/1.66 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.98/1.66 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.98/1.66 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.98/1.66 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Int_Oint ), X ) = X }.
% 0.98/1.66 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.98/1.66 ( tc_Int_Oint ) ) = X }.
% 0.98/1.66 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.98/1.66 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.98/1.66 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.98/1.66 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.98/1.66 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.98/1.66 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.98/1.66 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.98/1.66 ) }.
% 0.98/1.66 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.98/1.66 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.98/1.66 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.98/1.66 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.98/1.66 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.98/1.66 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.98/1.66 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.66 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.98/1.66 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.66 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.98/1.66 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.98/1.66 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.66 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 0.98/1.66 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.98/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.98/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.98/1.66 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.98/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.66 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.98/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.66 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.98/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.98/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.66 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.98/1.66 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.98/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.98/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.66 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.98/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.98/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.98/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.98/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.66 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.66 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.98/1.66 Z ) ), Y ) ) }.
% 0.98/1.66 { c_Nat_Onat_Onat__size( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), T, Z ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), T, Y ), c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), Z, T ), c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Opoly__gcd( X, Y, T ) ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.98/1.66 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.66 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.98/1.66 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.98/1.66 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.98/1.66 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.98/1.66 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.98/1.66 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.98/1.66 .
% 0.98/1.66 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.66 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.98/1.66 Z ) ), U ), T ) = Y }.
% 0.98/1.66 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.98/1.66 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.66 ( X ), Z ), U ), Y ) }.
% 0.98/1.66 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.66 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.66 W ) ), U ), Y ) }.
% 0.98/1.66 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.66 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.66 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.66 ( X ), Z ), U ), Y ) }.
% 0.98/1.66 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.66 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.66 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.66 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.98/1.66 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.98/1.66 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.66 X, Y ) }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.66 X, Z, Y ) }.
% 0.98/1.66 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.98/1.66 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.66 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.98/1.66 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.66 , Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.98/1.66 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.98/1.66 X, Y ) ) }.
% 0.98/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.98/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.98/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.98/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.66 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.98/1.66 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.98/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.98/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.98/1.66 }.
% 0.98/1.66 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.98/1.66 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.98/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.98/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.98/1.66 }.
% 0.98/1.66 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.98/1.66 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.66 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.98/1.66 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 0.98/1.66 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 0.98/1.66 tc_Nat_Onat ) ) }.
% 0.98/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.98/1.66 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.98/1.66 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.98/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.98/1.66 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.98/1.66 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.98/1.66 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.98/1.66 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.66 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.66 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.98/1.66 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), Z, Y ), alpha60( X, Y, Z, T ), ! Y =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.66 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.98/1.66 tc_Polynomial_Opoly( X ), Z, Y ), alpha60( X, Y, Z, T ), ! hAPP(
% 0.98/1.66 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.98/1.66 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 0.98/1.66 .
% 0.98/1.66 { ! alpha60( X, Y, Z, T ), alpha62( X, Y, Z, T ), alpha58( X, Y, T ) }.
% 0.98/1.66 { ! alpha60( X, Y, Z, T ), alpha62( X, Y, Z, T ), ! hAPP(
% 0.98/1.66 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.66 { ! alpha62( X, Y, Z, T ), alpha60( X, Y, Z, T ) }.
% 0.98/1.66 { ! alpha58( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.98/1.66 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.66 alpha60( X, Y, Z, T ) }.
% 0.98/1.66 { ! alpha62( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.66 ( X ), Z, T ), alpha63( X, Y, Z, T ) }.
% 0.98/1.66 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, T ), alpha62( X, Y
% 0.98/1.66 , Z, T ) }.
% 0.98/1.66 { ! alpha63( X, Y, Z, T ), alpha62( X, Y, Z, T ) }.
% 0.98/1.66 { ! alpha63( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.98/1.66 ), skol11( X, Y, U, W ), Y ) }.
% 0.98/1.66 { ! alpha63( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.98/1.66 ), skol11( X, Y, U, T ), T ) }.
% 0.98/1.66 { ! alpha63( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.98/1.66 ( X ), skol11( X, Y, Z, T ), Z ) }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Y ), !
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, T ),
% 0.98/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Z ), alpha63( X, Y
% 0.98/1.66 , Z, T ) }.
% 0.98/1.66 { ! alpha58( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! alpha58( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha58( X, Y, Z
% 0.98/1.66 ) }.
% 0.98/1.66 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_Osize__class_Osize(
% 0.98/1.66 tc_Nat_Onat, X ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.66 ) ) }.
% 0.98/1.66 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.66 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.66 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.98/1.66 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.66 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.98/1.66 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.98/1.66 { c_Nat_Osize__class_Osize( tc_Nat_Onat, X ) = X }.
% 0.98/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.66 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.98/1.66 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.66 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.98/1.66 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.98/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.66 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.98/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 0.98/1.66 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 0.98/1.66 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.98/1.66 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 0.98/1.66 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.98/1.66 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.98/1.66 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.98/1.66 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.98/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.98/1.66 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.98/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.66 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.98/1.66 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.66 tc_Polynomial_Opoly( X ), Y ) }.
% 0.98/1.66 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Nat_Onat ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.66 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.66 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 0.98/1.66 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 0.98/1.66 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.66 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.98/1.66 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.98/1.66 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.98/1.66 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.98/1.66 { c_HOL_Obool_Obool__size( c_fTrue ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Nat_Onat ) }.
% 0.98/1.66 { c_HOL_Obool_Obool__size( c_fFalse ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Nat_Onat ) }.
% 0.98/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.98/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.66 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.98/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.98/1.66 X ) ) }.
% 0.98/1.66 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.66 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.98/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.98/1.66 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.66 ( X, Z, Y ) }.
% 0.98/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.98/1.66 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.98/1.66 ( X, Z, Y ) }.
% 0.98/1.66 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.66 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.66 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.66 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.66 , T ) ) }.
% 0.98/1.66 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.66 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.66 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.66 , T, Y ) ) }.
% 0.98/1.66 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.66 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.66 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.66 , Y, T ) ) }.
% 0.98/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.98/1.66 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.66 ( X, Z, Y ) }.
% 0.98/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.66 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.66 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.66 , T, Y ) ) }.
% 0.98/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.98/1.66 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.98/1.66 ( X, T, Y ) }.
% 0.98/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.66 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.66 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.66 , Y, Z ) ) }.
% 0.98/1.66 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.66 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.98/1.66 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.98/1.66 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.66 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.66 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.98/1.66 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.98/1.66 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.98/1.66 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.98/1.66 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.66 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.66 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.98/1.67 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.98/1.67 ( X, Y ), Z ) }.
% 0.98/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.67 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.98/1.67 ( X, Z ), Y ) }.
% 0.98/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.67 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.67 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Nat_Onat ), X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.98/1.67 .
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Nat_Onat ), X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.98/1.67 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.98/1.67 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.98/1.67 .
% 0.98/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.98/1.67 .
% 0.98/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.98/1.67 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.98/1.67 X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.67 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.98/1.67 }.
% 0.98/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.67 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.98/1.67 , X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.67 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.98/1.67 .
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.67 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.98/1.67 .
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.67 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.98/1.67 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.67 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.98/1.67 .
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.67 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.67 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.67 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.98/1.67 ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.67 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.98/1.67 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.98/1.67 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.98/1.67 { alpha59( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.98/1.67 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.98/1.67 { alpha59( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.98/1.67 ( X, Y ), Z ) ) }.
% 0.98/1.67 { ! alpha59( X, Y, Z ), alpha61( X, Y, Z ), Z = Y }.
% 0.98/1.67 { ! alpha59( X, Y, Z ), alpha61( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.98/1.67 ) ) }.
% 0.98/1.67 { ! alpha61( X, Y, Z ), alpha59( X, Y, Z ) }.
% 0.98/1.67 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha59( X, Y, Z ) }.
% 0.98/1.67 { ! alpha61( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.98/1.67 }.
% 0.98/1.67 { ! alpha61( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.98/1.67 X, Y ), Z ) ), alpha61( X, Y, Z ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 0.98/1.67 , Y ) ) = Y }.
% 0.98/1.67 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.98/1.67 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, Y, Z ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.98/1.67 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 0.98/1.67 ) ), Y ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.67 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.98/1.67 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.98/1.67 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.98/1.67 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 0.98/1.67 X, Y ) ) = Y }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.98/1.67 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( X ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.98/1.67 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.67 = Y }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.98/1.67 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.98/1.67 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.98/1.67 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 0.98/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 0.98/1.67 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.67 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 0.98/1.67 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.98/1.67 ) ), Z ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.98/1.67 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.98/1.67 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.98/1.67 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.98/1.67 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.98/1.67 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.67 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.67 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.67 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.67 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( X ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.67 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.67 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.98/1.67 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.98/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.98/1.67 .
% 0.98/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.98/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.98/1.67 .
% 0.98/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.67 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.67 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( X ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.67 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.67 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( X ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.67 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.67 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.67 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.67 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.98/1.67 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha6( X, Y, Z, T ),
% 0.98/1.67 alpha29( X, Y, Z, T ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z, T ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha29( X, Y, Z, T ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.67 { ! alpha29( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! alpha29( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.67 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha29( X, Y, Z, T ) }.
% 0.98/1.67 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.98/1.67 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.98/1.67 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha6( X, Y, Z, T ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha7( X, Y, Z, T ),
% 0.98/1.67 alpha30( X, Y, Z, T ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha7( X, Y, Z, T ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha30( X, Y, Z, T ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.67 { ! alpha30( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! alpha30( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.67 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha30( X, Y, Z, T ) }.
% 0.98/1.67 { ! alpha7( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.67 { ! alpha7( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.67 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha7( X, Y, Z, T ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.98/1.67 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.98/1.67 ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.98/1.67 ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.98/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.67 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.98/1.67 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.67 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.67 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.67 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.67 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.67 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.98/1.67 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( X ) ) }.
% 0.98/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.98/1.67 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , Z, Y ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.67 .
% 0.98/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.67 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , Y ) }.
% 0.98/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.67 , Y ) }.
% 0.98/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.67 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.67 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.67 .
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.98/1.67 ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 0.98/1.67 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.67 { ! alpha8( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.67 c_Nat_OSuc( X ) ) }.
% 0.98/1.67 { ! alpha8( X, Y ), Y = c_Nat_OSuc( skol12( Z, Y ) ) }.
% 0.98/1.67 { ! alpha8( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol12( X,
% 0.98/1.67 Y ), X ) }.
% 0.98/1.67 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.98/1.67 ), alpha8( X, Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.67 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol13( X ) ) }.
% 0.98/1.67 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.98/1.67 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Nat_Onat ), Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.98/1.67 tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.98/1.67 tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol14( X, Y ) ) ) }.
% 0.98/1.67 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.98/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.98/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.98/1.67 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.67 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.67 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.67 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.67 tc_Nat_Onat ), X ), Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.98/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.98/1.67 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.98/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.98/1.67 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Nat_Onat ), Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.98/1.67 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Nat_Onat ), Z ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.98/1.67 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.98/1.67 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.98/1.67 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.67 Y ), X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.67 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.98/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.98/1.67 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.98/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.98/1.67 ), X ) ) }.
% 0.98/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.67 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.98/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.67 tc_Nat_Onat, Z, X ), Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.67 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.98/1.67 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.98/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.98/1.67 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.67 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.98/1.67 ), X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.98/1.67 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.98/1.67 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.67 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.98/1.67 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.98/1.67 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 0.98/1.67 .
% 0.98/1.67 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.98/1.67 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.98/1.67 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.98/1.67 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.98/1.67 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.98/1.67 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.98/1.67 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.98/1.67 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.98/1.67 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 0.98/1.67 }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.98/1.67 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 0.98/1.67 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.98/1.67 Y ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.98/1.67 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 0.98/1.67 ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.67 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.98/1.67 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.67 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.67 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.67 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.98/1.67 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.67 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.98/1.67 ( X, Z, W ) ), U ), Y ) ) }.
% 0.98/1.67 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.98/1.67 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.67 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.67 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.98/1.67 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.67 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.67 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.67 X, W, Z ) ), U ), T ), Y ) }.
% 0.98/1.67 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.67 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.67 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.67 ( X ), Z ), U ), Y ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.98/1.67 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.98/1.67 ) ) = X }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.98/1.67 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.67 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 0.98/1.67 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.67 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.98/1.67 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.98/1.67 , ! alpha9( X, Y, Z ) }.
% 0.98/1.67 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.98/1.67 , ! alpha31( X, Y, Z ) }.
% 0.98/1.67 { alpha9( X, Y, Z ), alpha31( X, Y, Z ), hBOOL( hAPP( Z,
% 0.98/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.67 { ! alpha31( X, Y, Z ), ! hBOOL( hAPP( Z, skol15( T, U, Z ) ) ) }.
% 0.98/1.67 { ! alpha31( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.98/1.67 skol15( X, Y, Z ) ) }.
% 0.98/1.67 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.98/1.67 ) ), alpha31( X, Y, Z ) }.
% 0.98/1.67 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 0.98/1.67 .
% 0.98/1.67 { ! alpha9( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Nat_Onat ) ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha9( X, Y, Z ) }.
% 0.98/1.67 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.98/1.67 , alpha10( X, Y, Z ) }.
% 0.98/1.67 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.98/1.67 , alpha32( X, Y, Z ) }.
% 0.98/1.67 { ! alpha10( X, Y, Z ), ! alpha32( X, Y, Z ), hBOOL( hAPP( Z,
% 0.98/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.67 { ! alpha32( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.98/1.67 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.98/1.67 { ! hBOOL( hAPP( Z, skol16( T, U, Z ) ) ), alpha32( X, Y, Z ) }.
% 0.98/1.67 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol16( X, Y, Z ) ),
% 0.98/1.67 alpha32( X, Y, Z ) }.
% 0.98/1.67 { ! alpha10( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.98/1.67 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.98/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha10( X, Y, Z ) }
% 0.98/1.67 .
% 0.98/1.67 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha10
% 0.98/1.67 ( X, Y, Z ) }.
% 0.98/1.67 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.67 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 0.98/1.67 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 0.98/1.67 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.98/1.67 Y ) ), c_Groups_Ominus__class_Ominus( X, Y, Z ) ) ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.98/1.67 c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.67 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.98/1.67 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.98/1.67 ( X ), Y ), Z ) ) }.
% 0.98/1.67 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.98/1.67 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.98/1.67 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.98/1.67 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.98/1.67 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 0.98/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.98/1.67 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.98/1.67 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 0.98/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.98/1.67 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.98/1.67 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.98/1.67 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.98/1.67 ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.67 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.98/1.67 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.67 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.98/1.67 .
% 0.98/1.67 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.98/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.98/1.67 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.67 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.98/1.67 = X }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.67 tc_Int_Oint ) ) ) }.
% 0.98/1.67 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.67 tc_Int_Oint ) ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.98/1.67 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.67 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.98/1.67 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.98/1.67 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.67 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.67 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.98/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.67 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.98/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.98/1.67 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.98/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.67 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.98/1.67 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.98/1.67 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 0.98/1.67 , Y = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.67 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 0.98/1.67 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 0.98/1.67 = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.98/1.67 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.98/1.67 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.98/1.67 , Y ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.98/1.67 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.98/1.67 .
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( X ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.67 .
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.98/1.67 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Nat_Onat ), Y ) }.
% 0.98/1.67 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.98/1.67 ), X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.98/1.67 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 0.98/1.67 }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.98/1.67 , alpha47( X, Y, Z, T ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 0.98/1.67 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha47( X, Y, Z, T ),
% 0.98/1.67 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 0.98/1.67 { ! alpha47( X, Y, Z, T ), alpha11( X, Z, T ) }.
% 0.98/1.67 { ! alpha47( X, Y, Z, T ), alpha33( X, Y, T ) }.
% 0.98/1.67 { ! alpha11( X, Z, T ), ! alpha33( X, Y, T ), alpha47( X, Y, Z, T ) }.
% 0.98/1.67 { ! alpha33( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ), alpha48( X, Y, Z ) }.
% 0.98/1.67 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha33( X
% 0.98/1.67 , Y, Z ) }.
% 0.98/1.67 { ! alpha48( X, Y, Z ), alpha33( X, Y, Z ) }.
% 0.98/1.67 { ! alpha48( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.67 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 0.98/1.67 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha48( X
% 0.98/1.67 , Y, Z ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 0.98/1.67 ), c_Polynomial_Odegree( X, Z ) ), alpha48( X, Y, Z ) }.
% 0.98/1.67 { ! alpha11( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.67 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha11( X,
% 0.98/1.67 Y, Z ) }.
% 0.98/1.67 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha11( X
% 0.98/1.67 , Y, Z ) }.
% 0.98/1.67 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 0.98/1.67 .
% 0.98/1.67 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.98/1.67 , c_Polynomial_Opdivmod__rel( X, c_Polynomial_Osmult( X, W, U ), T,
% 0.98/1.67 c_Polynomial_Osmult( X, W, Z ), c_Polynomial_Osmult( X, W, Y ) ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.98/1.67 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.98/1.67 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.98/1.67 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.98/1.67 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.98/1.67 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 0.98/1.67 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 0.98/1.67 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 0.98/1.67 ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.98/1.67 c_Polynomial_Opdivmod__rel( X, W, U, T, Z ), c_Polynomial_Opdivmod__rel(
% 0.98/1.67 X, W, c_Polynomial_Osmult( X, Y, U ), c_Polynomial_Osmult( X,
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ), T ), Z ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.98/1.67 , T = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! V0 =
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.67 c_Polynomial_OpCons( X, W, Y ) ), c_Polynomial_Odegree( X, T ) ), hAPP(
% 0.98/1.67 c_Polynomial_Ocoeff( X, T ), c_Polynomial_Odegree( X, T ) ) ),
% 0.98/1.67 c_Polynomial_Opdivmod__rel( X, c_Polynomial_OpCons( X, W, U ), T,
% 0.98/1.67 c_Polynomial_OpCons( X, V0, Z ), c_Groups_Ominus__class_Ominus(
% 0.98/1.67 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, W, Y ),
% 0.98/1.67 c_Polynomial_Osmult( X, V0, T ) ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha12( X, Y, Z ), alpha34
% 0.98/1.67 ( X, Y, Z ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha12( X, Y, Z
% 0.98/1.67 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha34( X, Y, Z
% 0.98/1.67 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.67 { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.67 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 ), alpha34( X, Y, Z ) }.
% 0.98/1.67 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.67 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.67 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.67 ), alpha12( X, Y, Z ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 0.98/1.67 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha13( X, Y, Z ), alpha35( X,
% 0.98/1.67 Y, Z ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha13( X, Y, Z
% 0.98/1.67 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.67 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha35( X, Y, Z
% 0.98/1.67 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.67 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.67 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.67 ), alpha35( X, Y, Z ) }.
% 0.98/1.67 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.67 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.67 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 ), alpha13( X, Y, Z ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.98/1.67 , Y, Z ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.98/1.67 , Y, Z ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.98/1.67 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha36( X, Y, Z, T ) }.
% 0.98/1.67 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha14( X, Y, T ) }.
% 0.98/1.67 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha36( X, Y, Z, T ), !
% 0.98/1.67 alpha14( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.98/1.67 { ! alpha36( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 0.98/1.67 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.98/1.67 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha36( X, Y, Z, T ) }.
% 0.98/1.67 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha36(
% 0.98/1.67 X, Y, Z, T ) }.
% 0.98/1.67 { ! alpha14( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { Y = c_Groups_Ozero__class_Ozero( X ), alpha14( X, Y, Z ) }.
% 0.98/1.67 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha14( X, Y, Z ) }.
% 0.98/1.67 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha37( X, Y, Z, T ) }.
% 0.98/1.67 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha15( X, Y, Z ) }.
% 0.98/1.67 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha37( X, Y, Z, T ), !
% 0.98/1.67 alpha15( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 0.98/1.67 { ! alpha37( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 0.98/1.67 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.98/1.67 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha37( X, Y, Z, T ) }.
% 0.98/1.67 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha37(
% 0.98/1.67 X, Y, Z, T ) }.
% 0.98/1.67 { ! alpha15( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { Z = c_Groups_Ozero__class_Ozero( X ), alpha15( X, Y, Z ) }.
% 0.98/1.67 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha15( X, Y, Z ) }.
% 0.98/1.67 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.98/1.67 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 0.98/1.67 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.98/1.67 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.98/1.67 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 0.98/1.67 ( X ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.98/1.67 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.98/1.67 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.67 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.67 , Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.98/1.67 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 0.98/1.67 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.67 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 0.98/1.67 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.67 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 0.98/1.67 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.98/1.67 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.67 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.98/1.67 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.67 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.67 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 }.
% 0.98/1.67 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.98/1.67 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 0.98/1.67 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.67 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.67 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.67 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 0.98/1.67 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 0.98/1.67 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.98/1.67 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.67 ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.67 ), Y ) }.
% 0.98/1.67 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 0.98/1.67 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.67 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 0.98/1.67 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.67 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.67 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.98/1.67 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.98/1.67 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.67 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.67 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Y, Z ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.98/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Z
% 0.98/1.67 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) }
% 0.98/1.67 .
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.98/1.67 Y ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X )
% 0.98/1.67 , Y ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.67 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.67 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.67 Y ), Z ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.67 Z, Y ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.67 Z, Y ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.67 Y ), Z ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.67 Y ), Z ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.67 Z, Y ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.67 Z ), Y ), alpha38( X, Y, Z, T ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.67 Z ), Y ), alpha49( X, Y, Z, T ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha38( X, Y, Z
% 0.98/1.67 , T ), ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.98/1.67 { ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Z ), alpha52( X, Y, Z, T ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.67 , alpha49( X, Y, Z, T ) }.
% 0.98/1.67 { ! alpha52( X, Y, Z, T ), alpha49( X, Y, Z, T ) }.
% 0.98/1.67 { ! alpha52( X, Y, Z, T ), alpha55( X, Y, Z, T ) }.
% 0.98/1.67 { ! alpha52( X, Y, Z, T ), alpha16( X, Y, Z ) }.
% 0.98/1.67 { ! alpha55( X, Y, Z, T ), ! alpha16( X, Y, Z ), alpha52( X, Y, Z, T ) }.
% 0.98/1.67 { ! alpha55( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.98/1.67 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.67 alpha55( X, Y, Z, T ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha55( X, Y, Z, T )
% 0.98/1.67 }.
% 0.98/1.67 { ! alpha38( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.67 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.67 alpha38( X, Y, Z, T ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha38( X, Y, Z, T ) }.
% 0.98/1.67 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.67 , alpha16( X, Y, Z ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.98/1.67 , alpha16( X, Y, Z ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.67 Z, Y ) ), alpha39( X, Y, Z, T ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.67 Z, Y ) ), alpha50( X, Y, Z, T ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha39( X, Y, Z
% 0.98/1.67 , T ), ! alpha50( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.67 { ! alpha50( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Y ), alpha53( X, Y, Z, T ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.98/1.67 , alpha50( X, Y, Z, T ) }.
% 0.98/1.67 { ! alpha53( X, Y, Z, T ), alpha50( X, Y, Z, T ) }.
% 0.98/1.67 { ! alpha53( X, Y, Z, T ), alpha56( X, Y, Z, T ) }.
% 0.98/1.67 { ! alpha53( X, Y, Z, T ), alpha17( X, Y, T ) }.
% 0.98/1.67 { ! alpha56( X, Y, Z, T ), ! alpha17( X, Y, T ), alpha53( X, Y, Z, T ) }.
% 0.98/1.67 { ! alpha56( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.67 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.67 alpha56( X, Y, Z, T ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha56( X, Y, Z, T ) }.
% 0.98/1.67 { ! alpha39( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.98/1.67 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.67 alpha39( X, Y, Z, T ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha39( X, Y, Z, T )
% 0.98/1.67 }.
% 0.98/1.67 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.67 , alpha17( X, Y, Z ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.67 , alpha17( X, Y, Z ) }.
% 0.98/1.67 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 0.98/1.67 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.98/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 0.98/1.67 .
% 0.98/1.67 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 0.98/1.67 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.98/1.67 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 0.98/1.67 .
% 0.98/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.67 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.67 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.67 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.67 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.98/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.98/1.67 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.67 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.98/1.67 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.67 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 0.98/1.67 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 0.98/1.67 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.67 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.67 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.67 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 0.98/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) }
% 0.98/1.67 .
% 0.98/1.67 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.98/1.67 c_Rings_Oinverse__class_Oinverse( X, Z ) ), T ) =
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.98/1.67 Y ) ), c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus
% 0.98/1.67 ( X, Y, Z ), T ) ) ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 0.98/1.67 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T, Z ), Y ) =
% 0.98/1.67 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.98/1.67 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 0.98/1.67 tc_Polynomial_Opoly( X ), Z, Y ) ), c_Polynomial_Osmult( X,
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 0.98/1.67 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 0.98/1.67 tc_Polynomial_Opoly( X ), Z, Y ) ) ), c_Polynomial_Odegree( X, Y ) ),
% 0.98/1.67 hAPP( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y )
% 0.98/1.67 ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.98/1.67 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.98/1.67 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.98/1.67 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.98/1.67 alpha18( X, Y, Z ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.98/1.67 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! alpha18( X, Y, Z ),
% 0.98/1.67 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.98/1.67 { ! alpha18( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.67 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.67 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.67 alpha18( X, Y, Z ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T,
% 0.98/1.67 c_Polynomial_Osmult( X, Y, Z ) ) = c_Divides_Odiv__class_Omod(
% 0.98/1.67 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.98/1.67 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.98/1.67 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 0.98/1.67 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Omod(
% 0.98/1.67 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.98/1.67 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.98/1.67 tc_Polynomial_Opoly( X ), Y ) ) = c_Divides_Odiv__class_Omod(
% 0.98/1.67 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.98/1.67 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.67 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.67 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.98/1.67 ( X ), Z, Y ) ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.98/1.67 , c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.98/1.67 c_Polynomial_Opoly__gcd( X, Y, c_Divides_Odiv__class_Omod(
% 0.98/1.67 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.98/1.67 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.98/1.67 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.98/1.67 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.98/1.67 .
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 0.98/1.67 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.98/1.67 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 0.98/1.67 tc_Polynomial_Opoly( X ), Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.67 c_Polynomial_Odegree( X, c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.98/1.67 ( X ), Z, Y ) ), c_Polynomial_Odegree( X, Y ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.98/1.67 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.98/1.67 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 0.98/1.67 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 0.98/1.67 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 0.98/1.67 c_Polynomial_Opoly__gcd( X, Z, c_Divides_Odiv__class_Omod(
% 0.98/1.67 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.67 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.67 X ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 0.98/1.67 Z ) = c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.67 ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.67 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.67 X ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) ), Y ) =
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.98/1.67 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) =
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), c_Rings_Odvd__class_Odvd
% 0.98/1.67 ( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, X ) ) }
% 0.98/1.67 .
% 0.98/1.67 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus
% 0.98/1.67 ( tc_Int_Oint, Z, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y )
% 0.98/1.67 = c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) }.
% 0.98/1.67 { ! c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.67 { c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.98/1.67 c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.67 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol17( X, Y ) ) }.
% 0.98/1.67 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 0.98/1.67 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.67 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol18( X, Y ) ) }.
% 0.98/1.67 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 0.98/1.67 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.67 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 0.98/1.67 ), Y ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 0.98/1.67 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.67 ( tc_Int_Oint, Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.98/1.67 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 0.98/1.67 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 0.98/1.67 }.
% 0.98/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 0.98/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 0.98/1.67 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Divides_Odiv__class_Omod(
% 0.98/1.67 tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X ),
% 0.98/1.67 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.98/1.67 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.98/1.67 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.98/1.67 tc_Int_Oint, Y, c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.67 ( tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.67 ( tc_Int_Oint, Y ), X ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.67 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.98/1.67 ( tc_Int_Oint, Y, X ) ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.98/1.67 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) ) }
% 0.98/1.67 .
% 0.98/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.98/1.67 tc_Int_Oint, Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.98/1.67 tc_Int_Oint, Z, Y ), X ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.98/1.67 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ), X ), Y ) =
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.98/1.67 tc_Int_Oint, Z, X ), Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.98/1.67 ( tc_Int_Oint, Y, X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.98/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.98/1.67 tc_Nat_Onat, Y, X ), X ) }.
% 0.98/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.98/1.67 tc_Nat_Onat, Y, X ), X ) }.
% 0.98/1.67 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.98/1.67 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.98/1.67 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.98/1.67 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.98/1.67 ( tc_Int_Oint, Y, X ) ) }.
% 0.98/1.67 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.98/1.67 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.98/1.67 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.67 c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.98/1.67 tc_Int_Oint, Y, X ), X ) }.
% 0.98/1.67 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.98/1.67 alpha19( X, Y, Z ) }.
% 0.98/1.67 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.98/1.67 alpha40( X, Y, Z ) }.
% 0.98/1.67 { ! alpha19( X, Y, Z ), ! alpha40( X, Y, Z ), hBOOL( hAPP( Z,
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.67 { ! alpha40( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.67 alpha51( X, Y, Z ) }.
% 0.98/1.67 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha40( X, Y, Z ) }.
% 0.98/1.67 { ! alpha51( X, Y, Z ), alpha40( X, Y, Z ) }.
% 0.98/1.67 { ! alpha51( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.98/1.67 ), alpha54( X, Y, Z, T ) }.
% 0.98/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol19( X, T, U ), X ),
% 0.98/1.67 alpha51( X, Y, Z ) }.
% 0.98/1.67 { ! alpha54( X, Y, Z, skol19( X, Y, Z ) ), alpha51( X, Y, Z ) }.
% 0.98/1.67 { ! alpha54( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.98/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.98/1.67 hBOOL( hAPP( Z, T ) ) }.
% 0.98/1.67 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol20( X, Y, T ) ), T
% 0.98/1.67 ), alpha54( X, Y, Z, T ) }.
% 0.98/1.67 { ! hBOOL( hAPP( Z, T ) ), alpha54( X, Y, Z, T ) }.
% 0.98/1.67 { ! alpha19( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.67 hBOOL( hAPP( Z, Y ) ) }.
% 0.98/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha19( X, Y, Z ) }.
% 0.98/1.67 { ! hBOOL( hAPP( Z, Y ) ), alpha19( X, Y, Z ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.98/1.67 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, T, X ) ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.98/1.67 tc_Nat_Onat ), X ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X )
% 0.98/1.67 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.67 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 0.98/1.67 X, Z, Y ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.98/1.67 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.98/1.67 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.98/1.67 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.67 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 0.98/1.67 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.98/1.67 ), Z ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 0.98/1.67 , Y ) ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.98/1.67 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.67 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.98/1.67 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.67 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.98/1.67 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.67 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 0.98/1.67 ( X, Z, Y ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.98/1.67 ( X, Y, Z ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.98/1.67 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 0.98/1.67 , Y ) ), Y ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.98/1.67 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.98/1.67 ), Z ), Y ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.98/1.67 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.98/1.67 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.98/1.67 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.67 T, Z ), Y ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 0.98/1.67 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.67 T, Y ), Z ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.98/1.67 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.98/1.67 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 0.98/1.67 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 0.98/1.67 ), Z ) }.
% 0.98/1.67 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.98/1.67 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 0.98/1.67 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 0.98/1.67 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 0.98/1.67 , U ), Z ) }.
% 0.98/1.67 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.67 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.98/1.67 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.98/1.67 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 0.98/1.67 Y ) ), Y ) }.
% 0.98/1.67 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.67 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.98/1.67 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.98/1.67 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 0.98/1.67 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.67 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.98/1.67 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.98/1.67 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.98/1.67 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.98/1.67 ( X, c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Omod( X, Z
% 0.98/1.67 , Y ) ), Y ) }.
% 0.98/1.67 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.98/1.67 = c_Divides_Odiv__class_Omod( X, Y, Z ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( X, T ), Z ) = c_Divides_Odiv__class_Omod
% 0.98/1.67 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, T,
% 0.98/1.67 c_Divides_Odiv__class_Omod( X, Z, Y ) ), ! c_Rings_Odvd__class_Odvd( X, T
% 0.98/1.67 , Y ), c_Rings_Odvd__class_Odvd( X, T, Z ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.67 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 0.98/1.67 , c_Divides_Odiv__class_Omod( X, Y, T ) ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.67 ), c_Divides_Odiv__class_Omod( X, c_Divides_Odiv__class_Omod( X, T, Y )
% 0.98/1.67 , Z ) = c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.67 ), ! c_Rings_Odvd__class_Odvd( X, Z, c_Divides_Odiv__class_Omod( X, T, Y
% 0.98/1.67 ) ), c_Rings_Odvd__class_Odvd( X, Z, T ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.67 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 0.98/1.67 , c_Divides_Odiv__class_Omod( X, T, Y ) ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.98/1.67 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.98/1.67 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 0.98/1.67 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 0.98/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 0.98/1.67 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.67 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.98/1.67 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 0.98/1.67 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.98/1.67 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.67 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 0.98/1.67 ( X ) ) ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.67 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.98/1.67 tc_Int_Oint, Z, X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.67 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, X ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.98/1.67 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.98/1.67 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( X ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Int_Oint ) ) = X }.
% 0.98/1.67 { Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.98/1.67 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.67 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.98/1.67 ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ), X ) =
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) }.
% 0.98/1.67 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.67 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, Y ) ), Y ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) ), X ) =
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.67 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 0.98/1.67 ( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.98/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) =
% 0.98/1.67 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.98/1.67 ( tc_Int_Oint, X, Y ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.98/1.67 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Int_Oint ), Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.98/1.67 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.98/1.67 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.67 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.98/1.67 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.67 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 0.98/1.67 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.98/1.67 }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.98/1.67 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.98/1.67 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y,
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.67 ( tc_Int_Oint, Y ), X ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.67 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.67 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 0.98/1.67 , c_Divides_Odiv__class_Odiv( X, Y, Z ), c_Divides_Odiv__class_Odiv( X, T
% 0.98/1.67 , Z ) ), c_Rings_Odvd__class_Odvd( X, Y, T ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.67 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 0.98/1.67 , Y, T ), c_Rings_Odvd__class_Odvd( X, c_Divides_Odiv__class_Odiv( X, Y,
% 0.98/1.67 Z ), c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.98/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 0.98/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.67 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 0.98/1.67 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.98/1.67 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.98/1.67 ( c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 0.98/1.67 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.98/1.67 c_Divides_Odiv__class_Odiv( X, Y, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.98/1.67 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 0.98/1.67 , Z ) ) }.
% 0.98/1.67 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.98/1.67 c_Divides_Odiv__class_Odiv( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z
% 0.98/1.67 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 0.98/1.67 , Z ) ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.67 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Divides_Odiv__class_Odiv( X
% 0.98/1.67 , c_Groups_Oplus__class_Oplus( X, Y, T ), Z ) =
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Y, Z ),
% 0.98/1.67 c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.67 ), ! c_Rings_Odvd__class_Odvd( X, U, T ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.98/1.67 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 0.98/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.98/1.67 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.67 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.67 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.98/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.67 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.67 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), Z ) = Y }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.67 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 0.98/1.67 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = c_Divides_Odiv__class_Odiv( X,
% 0.98/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.98/1.67 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.98/1.67 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = Y }.
% 0.98/1.67 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.98/1.67 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.98/1.67 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.67 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.98/1.67 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.98/1.67 .
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.98/1.67 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.98/1.67 .
% 0.98/1.67 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.98/1.67 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.67 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.67 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.98/1.67 }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.98/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.98/1.67 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.98/1.67 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.98/1.67 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.98/1.67 ) }.
% 0.98/1.67 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.67 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.98/1.67 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.67 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.98/1.67 .
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.98/1.67 .
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.67 .
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.67 .
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.98/1.67 tc_Int_Oint, X, Y ), X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 0.98/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.98/1.67 tc_Int_Oint, Z, Y ), X ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.98/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.98/1.67 ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.98/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.98/1.67 ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 0.98/1.67 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.98/1.67 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 0.98/1.67 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.98/1.67 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 0.98/1.67 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), !
% 0.98/1.67 c_Divides_Odiv__class_Odiv( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U
% 0.98/1.67 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP(
% 0.98/1.67 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 0.98/1.67 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), ! hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 0.98/1.67 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! c_Divides_Odiv__class_Odiv( X
% 0.98/1.67 , Z, Y ) = T, Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y
% 0.98/1.67 ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! Z = hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ), c_Divides_Odiv__class_Odiv
% 0.98/1.67 ( X, Z, Y ) = T }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.67 ( X ), c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ) =
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.67 ( X ), T ), c_Divides_Odiv__class_Odiv( X, Z, T ) ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( X, Z, T ) ), Y ) =
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X
% 0.98/1.67 , Z, Y ) ), Y ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.98/1.67 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), c_Divides_Odiv__class_Omod( X, Y
% 0.98/1.67 , Z ) ) = Y }.
% 0.98/1.67 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.67 c_Divides_Odiv__class_Omod( X, Z, Y ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 0.98/1.67 ), Y ) ) = Z }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.98/1.67 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.98/1.67 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.98/1.67 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, hAPP(
% 0.98/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.98/1.67 tc_Int_Oint, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y
% 0.98/1.67 ) ) }.
% 0.98/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.67 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.98/1.67 ( tc_Int_Oint, Y, X ) ) }.
% 0.98/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.67 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.67 c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.98/1.67 ( tc_Int_Oint, Y, X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.98/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.67 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.98/1.67 ( tc_Int_Oint, Y, X ) ) }.
% 0.98/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.67 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.98/1.67 c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.98/1.67 ( tc_Int_Oint, Y, X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.98/1.67 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.67 .
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.98/1.67 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.98/1.67 }.
% 0.98/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.67 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.98/1.67 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.98/1.67 }.
% 0.98/1.67 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.67 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.67 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.67 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.67 c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha20( X, Y, T,
% 0.98/1.67 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha20( X, Y, skol21( X, Y
% 0.98/1.67 , Z ), skol26( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.98/1.67 skol21( X, Y, Z ) ), skol26( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.98/1.67 { ! alpha20( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T
% 0.98/1.67 ) }.
% 0.98/1.67 { ! alpha20( X, Y, Z, T ), alpha41( X, Y, Z, T ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha41( X, Y, Z
% 0.98/1.67 , T ), alpha20( X, Y, Z, T ) }.
% 0.98/1.67 { ! alpha41( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.67 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.67 { ! alpha41( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.98/1.67 .
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha41( X,
% 0.98/1.67 Y, Z, T ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv
% 0.98/1.67 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X )
% 0.98/1.67 ) ), ! alpha21( X, Y, T, U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Int_Oint ), X ), alpha21( X, Y, skol22( X, Y, Z ), skol27( X, Y, Z )
% 0.98/1.67 ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X )
% 0.98/1.67 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, skol22( X, Y, Z ) ), skol27
% 0.98/1.67 ( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.98/1.67 tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 0.98/1.67 ) }.
% 0.98/1.67 { ! alpha21( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ) }.
% 0.98/1.67 { ! alpha21( X, Y, Z, T ), alpha42( X, Y, Z, T ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha42( X, Y, Z, T )
% 0.98/1.67 , alpha21( X, Y, Z, T ) }.
% 0.98/1.67 { ! alpha42( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.98/1.67 ) }.
% 0.98/1.67 { ! alpha42( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.98/1.67 .
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha42( X,
% 0.98/1.67 Y, Z, T ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.67 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.98/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.98/1.67 tc_Nat_Onat, Z, X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.67 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, X ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.98/1.67 tc_Int_Oint, X, Y ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.67 tc_Int_Oint, X, Y ) ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.98/1.67 tc_Nat_Onat, Z, Y ), X ) }.
% 0.98/1.67 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.98/1.67 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 0.98/1.67 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Odiv(
% 0.98/1.67 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.98/1.67 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.67 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 0.98/1.67 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.98/1.67 ( X ), T, Z ), Y ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.98/1.67 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.98/1.67 tc_Polynomial_Opoly( X ), Y ) ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.67 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.98/1.67 ( X ), Z, Y ) ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.98/1.67 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.67 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.67 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.98/1.67 ( X ), Z, Y ) ) }.
% 0.98/1.67 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.67 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.98/1.67 , c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 0.98/1.67 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Z, Y,
% 0.98/1.67 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ),
% 0.98/1.67 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.98/1.67 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.67 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( X ) ) }.
% 0.98/1.67 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.67 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.67 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.67 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.67 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.67 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.67 { ! class_Rings_Oordered__semiring( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.67 { ! class_Rings_Oordered__semiring( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.67 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.67 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.67 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.98/1.67 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.67 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.67 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.98/1.67 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.67 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.67 { ! class_Rings_Oordered__semiring( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.67 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.67 { ! class_Rings_Oordered__semiring( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.67 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.67 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.67 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.67 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.67 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( X ) ) }.
% 0.98/1.67 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.67 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.67 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( X ) ), alpha22( X, Y, Z ), alpha43( X, Y, Z ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha22( X, Y, Z ),
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( X ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha43( X, Y, Z ),
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( X ) ) }.
% 0.98/1.67 { ! alpha43( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! alpha43( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.67 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.98/1.67 ( X ), Y ), alpha43( X, Y, Z ) }.
% 0.98/1.67 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.67 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ), alpha22( X, Y, Z ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha23( X, Y
% 0.98/1.67 , Z ), alpha44( X, Y, Z ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha23( X, Y, Z ),
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha44( X, Y, Z ),
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.67 { ! alpha44( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! alpha44( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.67 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ), alpha44( X, Y, Z ) }.
% 0.98/1.67 { ! alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.67 { ! alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Y ), alpha23( X, Y, Z ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.67 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.98/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.67 ) }.
% 0.98/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.67 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.98/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.67 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 ) }.
% 0.98/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.98/1.67 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.98/1.67 ) }.
% 0.98/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.98/1.67 .
% 0.98/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.98/1.67 .
% 0.98/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.67 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.98/1.67 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.67 Y, Z ) ) }.
% 0.98/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.67 Z, Y ) ) }.
% 0.98/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.67 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.98/1.67 ) ) }.
% 0.98/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.98/1.67 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.98/1.67 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ),
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.67 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.98/1.67 ( X, Y ), Y ) }.
% 0.98/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.67 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.67 ) }.
% 0.98/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.98/1.67 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.98/1.67 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 ) }.
% 0.98/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.67 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.67 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.98/1.67 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.98/1.67 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.67 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha24( X, Y, Z ), alpha45
% 0.98/1.67 ( X, Y, Z ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha24( X, Y, Z
% 0.98/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.67 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha45( X, Y, Z
% 0.98/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.67 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.67 { ! alpha45( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! alpha45( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.67 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ) ), alpha45( X, Y, Z ) }.
% 0.98/1.67 { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.67 { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.67 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.67 c_Groups_Ozero__class_Ozero( X ), Y ), alpha24( X, Y, Z ) }.
% 0.98/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.68 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha25( X, Y, Z ), alpha46
% 0.98/1.68 ( X, Y, Z ) }.
% 0.98/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha25( X, Y, Z
% 0.98/1.68 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.98/1.68 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha46( X, Y, Z
% 0.98/1.68 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.98/1.68 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.68 { ! alpha46( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.68 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.68 { ! alpha46( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.68 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.68 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.68 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.98/1.68 ( X ), Y ), alpha46( X, Y, Z ) }.
% 0.98/1.68 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.68 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.68 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.68 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.68 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.68 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.68 c_Groups_Ozero__class_Ozero( X ) ), alpha25( X, Y, Z ) }.
% 0.98/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.68 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.98/1.68 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.98/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.68 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.98/1.68 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.98/1.68 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.68 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.68 ) }.
% 0.98/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.68 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.68 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.98/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.98/1.68 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.68 ) }.
% 0.98/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.68 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.98/1.68 ) ) }.
% 0.98/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.98/1.68 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 0.98/1.68 ( tc_Int_Oint, Y, X ), X = Y }.
% 0.98/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.68 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.98/1.68 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.68 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.98/1.68 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.98/1.68 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.68 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.68 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.98/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.98/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.98/1.68 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.98/1.68 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.98/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.98/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.98/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.98/1.68 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.68 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.98/1.68 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.68 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.68 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.68 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.98/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.68 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.68 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.98/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.68 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.68 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.68 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.68 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.68 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.98/1.68 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.68 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.68 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.68 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.68 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.68 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.68 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.68 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.98/1.68 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.68 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.68 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.68 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.98/1.68 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.68 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.68 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.68 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.68 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.98/1.68 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.68 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.68 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.68 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.68 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.68 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.68 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.68 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.68 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.68 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.68 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.68 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.98/1.68 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.98/1.68 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.98/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.98/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.98/1.68 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.98/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.68 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.98/1.68 .
% 0.98/1.68 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.98/1.68 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.68 , Y, T ) ) }.
% 0.98/1.68 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.98/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.98/1.68 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.98/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.68 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.98/1.68 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.98/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.68 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.98/1.68 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 0.98/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.68 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.98/1.68 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 0.98/1.68 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.98/1.68 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.98/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.98/1.68 tc_Nat_Onat, Y, X ), Y ) }.
% 0.98/1.68 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) =
% 0.98/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.68 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.98/1.68 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.68 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.98/1.68 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.98/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.98/1.68 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.98/1.68 tc_Nat_Onat, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y
% 0.98/1.68 ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.68 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.68 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.68 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.68 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.68 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.68 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.98/1.68 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.68 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.68 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.98/1.68 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.68 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.68 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.98/1.68 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.98/1.68 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.68 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.98/1.68 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.68 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.68 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.68 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.98/1.68 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.68 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.68 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.68 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.68 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.68 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.68 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.68 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.68 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.68 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.68 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.98/1.68 ) ) }.
% 0.98/1.68 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.98/1.68 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.98/1.68 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.98/1.68 tc_Int_Oint ) }.
% 0.98/1.68 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.68 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.98/1.68 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.68 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.98/1.68 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.98/1.68 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.98/1.68 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.98/1.68 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.98/1.68 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.98/1.68 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.98/1.68 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.98/1.68 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.98/1.68 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.98/1.68 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.98/1.68 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.98/1.68 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.98/1.68 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.98/1.68 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.98/1.68 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.98/1.68 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.98/1.68 { class_Power_Opower( tc_Int_Oint ) }.
% 0.98/1.68 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.98/1.68 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.98/1.68 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.98/1.68 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.98/1.68 tc_Nat_Onat ) }.
% 0.98/1.68 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.98/1.68 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.98/1.68 tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.98/1.68 { ! class_Rings_Oidom( X ),
% 0.98/1.68 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.68 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.98/1.68 ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.68 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.98/1.68 X ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.68 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.98/1.68 ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.68 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.68 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.68 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.68 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.98/1.68 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.68 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.68 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.68 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.68 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.98/1.68 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.98/1.68 ( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.98/1.68 ( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 0.98/1.68 ( X ) ) }.
% 0.98/1.68 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.98/1.68 }.
% 0.98/1.68 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.98/1.68 ) ) }.
% 0.98/1.68 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.98/1.68 .
% 0.98/1.68 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.98/1.68 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.68 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 0.98/1.68 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 0.98/1.68 { ! hBOOL( c_fFalse ) }.
% 0.98/1.68 { hBOOL( c_fTrue ) }.
% 0.98/1.68 { ! || }.
% 0.98/1.68
% 0.98/1.68 *** allocated 15000 integers for clauses
% 0.98/1.68 *** allocated 22500 integers for clauses
% 0.98/1.68 *** allocated 33750 integers for clauses
% 0.98/1.68 *** allocated 50625 integers for clauses
% 0.98/1.68 *** allocated 75937 integers for clauses
% 0.98/1.68 *** allocated 113905 integers for clauses
% 0.98/1.68 percentage equality = 0.320923, percentage horn = 0.876765
% 0.98/1.68 This is a problem with some equality
% 0.98/1.68
% 0.98/1.68
% 0.98/1.68
% 0.98/1.68 Options Used:
% 0.98/1.68
% 0.98/1.68 useres = 1
% 0.98/1.68 useparamod = 1
% 0.98/1.68 useeqrefl = 1
% 0.98/1.68 useeqfact = 1
% 0.98/1.68 usefactor = 1
% 0.98/1.68 usesimpsplitting = 0
% 0.98/1.68 usesimpdemod = 5
% 0.98/1.68 usesimpres = 3
% 0.98/1.68
% 0.98/1.68 resimpinuse = 1000
% 0.98/1.68 resimpclauses = 20000
% 0.98/1.68 substype = eqrewr
% 0.98/1.68 backwardsubs = 1
% 0.98/1.68 selectoldest = 5
% 0.98/1.68
% 0.98/1.68 litorderings [0] = split
% 0.98/1.68 litorderings [1] = extend the termordering, first sorting on arguments
% 0.98/1.68
% 0.98/1.68 termordering = kbo
% 0.98/1.68
% 0.98/1.68 litapriori = 0
% 0.98/1.68 termapriori = 1
% 0.98/1.68 litaposteriori = 0
% 0.98/1.68 termaposteriori = 0
% 0.98/1.68 demodaposteriori = 0
% 0.98/1.68 ordereqreflfact = 0
% 0.98/1.68
% 0.98/1.68 litselect = negord
% 0.98/1.68
% 0.98/1.68 maxweight = 15
% 0.98/1.68 maxdepth = 30000
% 0.98/1.68 maxlength = 115
% 0.98/1.68 maxnrvars = 195
% 0.98/1.68 excuselevel = 1
% 0.98/1.68 increasemaxweight = 1
% 0.98/1.68
% 0.98/1.68 maxselected = 10000000
% 0.98/1.68 maxnrclauses = 10000000
% 0.98/1.68
% 0.98/1.68 showgenerated = 0
% 0.98/1.68 showkept = 0
% 0.98/1.68 showselected = 0
% 0.98/1.68 showdeleted = 0
% 0.98/1.68 showresimp = 1
% 0.98/1.68 showstatus = 2000
% 0.98/1.68
% 0.98/1.68 prologoutput = 0
% 0.98/1.68 nrgoals = 5000000
% 0.98/1.68 totalproof = 1
% 0.98/1.68
% 0.98/1.68 Symbols occurring in the translation:
% 0.98/1.68
% 0.98/1.68 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.98/1.68 . [1, 2] (w:1, o:187, a:1, s:1, b:0),
% 0.98/1.68 || [2, 0] (w:1, o:3, a:1, s:1, b:0),
% 0.98/1.68 ! [4, 1] (w:0, o:105, a:1, s:1, b:0),
% 0.98/1.68 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.98/1.68 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.98/1.68 hAPP [38, 2] (w:1, o:211, a:1, s:1, b:0),
% 0.98/1.68 v_p [39, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.98/1.68 tc_Complex_Ocomplex [40, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.98/1.68 tc_Polynomial_Opoly [41, 1] (w:1, o:114, a:1, s:1, b:0),
% 0.98/1.68 c_Groups_Ozero__class_Ozero [42, 1] (w:1, o:115, a:1, s:1, b:0),
% 0.98/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [45, 3] (w:1, o:
% 0.98/1.68 236, a:1, s:1, b:0),
% 0.98/1.68 class_Groups_Ozero [48, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.98/1.68 class_Rings_Ocomm__semiring__0 [50, 1] (w:1, o:123, a:1, s:1, b:0),
% 0.98/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [51, 3] (w:1
% 0.98/1.68 , o:237, a:1, s:1, b:0),
% 0.98/1.68 c_Polynomial_Opoly__rec [55, 5] (w:1, o:325, a:1, s:1, b:0),
% 0.98/1.68 c_Polynomial_Opoly [56, 2] (w:1, o:212, a:1, s:1, b:0),
% 0.98/1.68 v_q [57, 0] (w:1, o:34, a:1, s:1, b:0),
% 0.98/1.68 c_Polynomial_Omonom [59, 3] (w:1, o:240, a:1, s:1, b:0),
% 0.98/1.68 c_Polynomial_Ocoeff [63, 2] (w:1, o:213, a:1, s:1, b:0),
% 0.98/1.68 c_Polynomial_Osmult [65, 3] (w:1, o:241, a:1, s:1, b:0),
% 0.98/1.68 class_Rings_Oidom [66, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.98/1.68 class_Int_Oring__char__0 [72, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.98/1.68 c_Polynomial_Oorder [74, 3] (w:1, o:242, a:1, s:1, b:0),
% 0.98/1.68 tc_Nat_Onat [75, 0] (w:1, o:57, a:1, s:1, b:0),
% 0.98/1.68 c_Polynomial_OpCons [77, 3] (w:1, o:243, a:1, s:1, b:0),
% 0.98/1.68 class_Fields_Ofield [78, 1] (w:1, o:116, a:1, s:1, b:0),
% 0.98/1.68 c_Rings_Odvd__class_Odvd [79, 3] (w:1, o:244, a:1, s:1, b:0),
% 0.98/1.68 c_Polynomial_Opcompose [81, 3] (w:1, o:245, a:1, s:1, b:0),
% 0.98/1.68 c_Polynomial_Odegree [82, 2] (w:1, o:214, a:1, s:1, b:0),
% 0.98/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [83, 2] (w:1, o:215
% 0.98/1.68 , a:1, s:1, b:0),
% 0.98/1.68 c_Power_Opower__class_Opower [84, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.98/1.68 c_Groups_Otimes__class_Otimes [85, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.98/1.68 v_r____ [86, 0] (w:1, o:60, a:1, s:1, b:0),
% 0.98/1.68 c_Groups_Oplus__class_Oplus [87, 3] (w:1, o:246, a:1, s:1, b:0),
% 0.98/1.68 class_Groups_Ocancel__semigroup__add [90, 1] (w:1, o:128, a:1, s:1
% 0.98/1.68 , b:0),
% 0.98/1.68 class_Groups_Ocancel__ab__semigroup__add [91, 1] (w:1, o:129, a:1, s:
% 0.98/1.68 1, b:0),
% 0.98/1.68 class_Groups_Ocomm__monoid__add [92, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.98/1.68
% 0.98/1.68 class_Groups_Oab__semigroup__mult [95, 1] (w:1, o:131, a:1, s:1, b:0)
% 0.98/1.68 ,
% 0.98/1.68 class_Groups_Oab__semigroup__add [96, 1] (w:1, o:132, a:1, s:1, b:0)
% 0.98/1.68 ,
% 0.98/1.68 class_Rings_Ocomm__semiring__1 [97, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.98/1.68 class_Groups_Omonoid__add [98, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.98/1.68 class_Groups_Olinordered__ab__group__add [99, 1] (w:1, o:134, a:1, s:
% 0.98/1.68 1, b:0),
% 0.98/1.68 c_fequal [100, 2] (w:1, o:216, a:1, s:1, b:0),
% 0.98/1.68 c_If [101, 4] (w:1, o:299, a:1, s:1, b:0),
% 0.98/1.68 class_Rings_Odvd [105, 1] (w:1, o:137, a:1, s:1, b:0),
% 0.98/1.68 class_Rings_Osemiring__0 [106, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.98/1.68 hBOOL [107, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.98/1.68 class_Power_Opower [108, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.98/1.68 class_Rings_Omult__zero [109, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.98/1.68 class_Rings_Ono__zero__divisors [110, 1] (w:1, o:153, a:1, s:1, b:0)
% 0.98/1.68 ,
% 0.98/1.68 class_Rings_Ozero__neq__one [111, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.98/1.68 class_Rings_Olinordered__ring__strict [112, 1] (w:1, o:145, a:1, s:1
% 0.98/1.68 , b:0),
% 0.98/1.68 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.98/1.68 114, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.98/1.68 class_Groups_Omonoid__mult [120, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.98/1.68 class_Rings_Oring__no__zero__divisors [121, 1] (w:1, o:138, a:1, s:1
% 0.98/1.68 , b:0),
% 0.98/1.68 class_Rings_Osemiring [124, 1] (w:1, o:155, a:1, s:1, b:0),
% 0.98/1.68 class_Rings_Ocomm__semiring [125, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.98/1.68 class_Rings_Oring__1__no__zero__divisors [128, 1] (w:1, o:139, a:1
% 0.98/1.68 , s:1, b:0),
% 0.98/1.68 class_Groups_Ocomm__monoid__mult [130, 1] (w:1, o:170, a:1, s:1, b:0)
% 0.98/1.68 ,
% 0.98/1.68 c_Polynomial_Osynthetic__div [131, 3] (w:1, o:247, a:1, s:1, b:0),
% 0.98/1.68 class_RealVector_Oreal__normed__algebra [134, 1] (w:1, o:156, a:1, s:
% 0.98/1.68 1, b:0),
% 0.98/1.68 class_Rings_Ocomm__ring__1 [142, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.98/1.68 c_Groups_Oone__class_Oone [143, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.98/1.68 c_Nat_OSuc [144, 1] (w:1, o:172, a:1, s:1, b:0),
% 0.98/1.68 class_Groups_Oone [147, 1] (w:1, o:173, a:1, s:1, b:0),
% 0.98/1.68 tc_Int_Oint [150, 0] (w:1, o:90, a:1, s:1, b:0),
% 0.98/1.68 c_Groups_Ouminus__class_Ouminus [151, 2] (w:1, o:217, a:1, s:1, b:0)
% 0.98/1.68 ,
% 0.98/1.68 c_Power_Opower_Opower [152, 3] (w:1, o:248, a:1, s:1, b:0),
% 0.98/1.68 class_Groups_Oab__group__add [158, 1] (w:1, o:174, a:1, s:1, b:0),
% 0.98/1.68 class_Rings_Ocomm__ring [159, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.98/1.68 class_Groups_Ogroup__add [160, 1] (w:1, o:175, a:1, s:1, b:0),
% 0.98/1.68 class_Rings_Oring [161, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.98/1.68 class_Rings_Oring__1 [162, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.98/1.68 c_Polynomial_Opoly__gcd [165, 3] (w:1, o:249, a:1, s:1, b:0),
% 0.98/1.68 c_Nat_Onat_Onat__size [170, 1] (w:1, o:176, a:1, s:1, b:0),
% 0.98/1.68 c_Groups_Ominus__class_Ominus [171, 3] (w:1, o:250, a:1, s:1, b:0),
% 0.98/1.68 c_Nat_Osize__class_Osize [174, 2] (w:1, o:218, a:1, s:1, b:0),
% 0.98/1.68 c_Rings_Oinverse__class_Oinverse [175, 2] (w:1, o:219, a:1, s:1, b:0)
% 0.98/1.68 ,
% 0.98/1.68 c_Orderings_Oord__class_Oless [176, 3] (w:1, o:238, a:1, s:1, b:0),
% 0.98/1.68 c_fTrue [177, 0] (w:1, o:99, a:1, s:1, b:0),
% 0.98/1.68 c_HOL_Obool_Obool__size [178, 1] (w:1, o:177, a:1, s:1, b:0),
% 0.98/1.68 c_fFalse [179, 0] (w:1, o:100, a:1, s:1, b:0),
% 0.98/1.68 class_Groups_Oordered__ab__semigroup__add__imp__le [180, 1] (w:1, o:
% 0.98/1.68 178, a:1, s:1, b:0),
% 0.98/1.68 class_Groups_Oordered__cancel__ab__semigroup__add [181, 1] (w:1, o:
% 0.98/1.68 179, a:1, s:1, b:0),
% 0.98/1.68 class_Groups_Oordered__ab__group__add [182, 1] (w:1, o:180, a:1, s:1
% 0.98/1.68 , b:0),
% 0.98/1.68 class_Rings_Odivision__ring__inverse__zero [186, 1] (w:1, o:157, a:1
% 0.98/1.68 , s:1, b:0),
% 0.98/1.68 class_Rings_Olinordered__idom [187, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.98/1.68 class_Rings_Odivision__ring [188, 1] (w:1, o:158, a:1, s:1, b:0),
% 0.98/1.68 class_Rings_Olinordered__semidom [189, 1] (w:1, o:148, a:1, s:1, b:0)
% 0.98/1.68 ,
% 0.98/1.68 class_Rings_Olinordered__comm__semiring__strict [191, 1] (w:1, o:149
% 0.98/1.68 , a:1, s:1, b:0),
% 0.98/1.68 class_Rings_Olinordered__semiring__strict [192, 1] (w:1, o:150, a:1
% 0.98/1.68 , s:1, b:0),
% 0.98/1.68 class_Rings_Olinordered__ring [193, 1] (w:1, o:147, a:1, s:1, b:0),
% 0.98/1.68 class_Groups_Oordered__comm__monoid__add [194, 1] (w:1, o:181, a:1
% 0.98/1.68 , s:1, b:0),
% 0.98/1.68 class_Rings_Oordered__ring [199, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.98/1.68 class_Fields_Olinordered__field [201, 1] (w:1, o:117, a:1, s:1, b:0)
% 0.98/1.68 ,
% 0.98/1.68 class_Fields_Olinordered__field__inverse__zero [202, 1] (w:1, o:118
% 0.98/1.68 , a:1, s:1, b:0),
% 0.98/1.68 class_Fields_Ofield__inverse__zero [203, 1] (w:1, o:119, a:1, s:1, b:
% 0.98/1.68 0),
% 0.98/1.68 c_Polynomial_Opdivmod__rel [205, 5] (w:1, o:326, a:1, s:1, b:0),
% 0.98/1.68 c_Rings_Oinverse__class_Odivide [212, 3] (w:1, o:251, a:1, s:1, b:0)
% 0.98/1.68 ,
% 0.98/1.68 class_RealVector_Oreal__normed__field [213, 1] (w:1, o:160, a:1, s:1
% 0.98/1.68 , b:0),
% 0.98/1.68 class_RealVector_Oreal__field [214, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.98/1.68 c_Divides_Odiv__class_Omod [215, 3] (w:1, o:252, a:1, s:1, b:0),
% 0.98/1.68 c_Polynomial_Opos__poly [216, 2] (w:1, o:220, a:1, s:1, b:0),
% 0.98/1.68 class_Divides_Osemiring__div [217, 1] (w:1, o:183, a:1, s:1, b:0),
% 0.98/1.68 class_Divides_Oring__div [220, 1] (w:1, o:182, a:1, s:1, b:0),
% 0.98/1.68 c_Divides_Odiv__class_Odiv [221, 3] (w:1, o:253, a:1, s:1, b:0),
% 0.98/1.68 c_Groups_Osgn__class_Osgn [222, 2] (w:1, o:221, a:1, s:1, b:0),
% 0.98/1.68 class_RealVector_Oreal__normed__algebra__1 [223, 1] (w:1, o:162, a:1
% 0.98/1.68 , s:1, b:0),
% 0.98/1.68 class_RealVector_Oreal__normed__vector [224, 1] (w:1, o:163, a:1, s:1
% 0.98/1.68 , b:0),
% 0.98/1.68 class_RealVector_Oreal__normed__div__algebra [225, 1] (w:1, o:164, a:
% 0.98/1.68 1, s:1, b:0),
% 0.98/1.68 class_Groups_Osgn__if [226, 1] (w:1, o:184, a:1, s:1, b:0),
% 0.98/1.68 c_Orderings_Oord__class_Oless__eq [227, 3] (w:1, o:239, a:1, s:1, b:0
% 0.98/1.68 ),
% 0.98/1.68 class_Rings_Oordered__cancel__semiring [228, 1] (w:1, o:165, a:1, s:1
% 0.98/1.68 , b:0),
% 0.98/1.68 class_Rings_Oordered__semiring [229, 1] (w:1, o:166, a:1, s:1, b:0),
% 4.59/4.96
% 4.59/4.96 class_Rings_Oordered__comm__semiring [230, 1] (w:1, o:167, a:1, s:1
% 4.59/4.96 , b:0),
% 4.59/4.96 class_Groups_Oordered__ab__semigroup__add [231, 1] (w:1, o:185, a:1
% 4.59/4.96 , s:1, b:0),
% 4.59/4.96 class_Rings_Olinordered__semiring [234, 1] (w:1, o:151, a:1, s:1, b:0
% 4.59/4.96 ),
% 4.59/4.96 class_Groups_Ocancel__comm__monoid__add [236, 1] (w:1, o:186, a:1, s:
% 4.59/4.96 1, b:0),
% 4.59/4.96 alpha1 [237, 3] (w:1, o:254, a:1, s:1, b:1),
% 4.59/4.96 alpha2 [238, 2] (w:1, o:222, a:1, s:1, b:1),
% 4.59/4.96 alpha3 [239, 2] (w:1, o:225, a:1, s:1, b:1),
% 4.59/4.96 alpha4 [240, 2] (w:1, o:226, a:1, s:1, b:1),
% 4.59/4.96 alpha5 [241, 2] (w:1, o:227, a:1, s:1, b:1),
% 4.59/4.96 alpha6 [242, 4] (w:1, o:306, a:1, s:1, b:1),
% 4.59/4.96 alpha7 [243, 4] (w:1, o:310, a:1, s:1, b:1),
% 4.59/4.96 alpha8 [244, 2] (w:1, o:228, a:1, s:1, b:1),
% 4.59/4.96 alpha9 [245, 3] (w:1, o:255, a:1, s:1, b:1),
% 4.59/4.96 alpha10 [246, 3] (w:1, o:256, a:1, s:1, b:1),
% 4.59/4.96 alpha11 [247, 3] (w:1, o:257, a:1, s:1, b:1),
% 4.59/4.96 alpha12 [248, 3] (w:1, o:258, a:1, s:1, b:1),
% 4.59/4.96 alpha13 [249, 3] (w:1, o:259, a:1, s:1, b:1),
% 4.59/4.96 alpha14 [250, 3] (w:1, o:260, a:1, s:1, b:1),
% 4.59/4.96 alpha15 [251, 3] (w:1, o:261, a:1, s:1, b:1),
% 4.59/4.96 alpha16 [252, 3] (w:1, o:262, a:1, s:1, b:1),
% 4.59/4.96 alpha17 [253, 3] (w:1, o:263, a:1, s:1, b:1),
% 4.59/4.96 alpha18 [254, 3] (w:1, o:264, a:1, s:1, b:1),
% 4.59/4.96 alpha19 [255, 3] (w:1, o:265, a:1, s:1, b:1),
% 4.59/4.96 alpha20 [256, 4] (w:1, o:311, a:1, s:1, b:1),
% 4.59/4.96 alpha21 [257, 4] (w:1, o:312, a:1, s:1, b:1),
% 4.59/4.96 alpha22 [258, 3] (w:1, o:266, a:1, s:1, b:1),
% 4.59/4.96 alpha23 [259, 3] (w:1, o:267, a:1, s:1, b:1),
% 4.59/4.96 alpha24 [260, 3] (w:1, o:268, a:1, s:1, b:1),
% 4.59/4.96 alpha25 [261, 3] (w:1, o:269, a:1, s:1, b:1),
% 4.59/4.96 alpha26 [262, 4] (w:1, o:313, a:1, s:1, b:1),
% 4.59/4.96 alpha27 [263, 2] (w:1, o:223, a:1, s:1, b:1),
% 4.59/4.96 alpha28 [264, 2] (w:1, o:224, a:1, s:1, b:1),
% 4.59/4.96 alpha29 [265, 4] (w:1, o:314, a:1, s:1, b:1),
% 4.59/4.96 alpha30 [266, 4] (w:1, o:315, a:1, s:1, b:1),
% 4.59/4.96 alpha31 [267, 3] (w:1, o:270, a:1, s:1, b:1),
% 4.59/4.96 alpha32 [268, 3] (w:1, o:271, a:1, s:1, b:1),
% 4.59/4.96 alpha33 [269, 3] (w:1, o:272, a:1, s:1, b:1),
% 4.59/4.96 alpha34 [270, 3] (w:1, o:273, a:1, s:1, b:1),
% 4.59/4.96 alpha35 [271, 3] (w:1, o:274, a:1, s:1, b:1),
% 4.59/4.96 alpha36 [272, 4] (w:1, o:316, a:1, s:1, b:1),
% 4.59/4.96 alpha37 [273, 4] (w:1, o:317, a:1, s:1, b:1),
% 4.59/4.96 alpha38 [274, 4] (w:1, o:318, a:1, s:1, b:1),
% 4.59/4.96 alpha39 [275, 4] (w:1, o:319, a:1, s:1, b:1),
% 4.59/4.96 alpha40 [276, 3] (w:1, o:275, a:1, s:1, b:1),
% 4.59/4.96 alpha41 [277, 4] (w:1, o:320, a:1, s:1, b:1),
% 4.59/4.96 alpha42 [278, 4] (w:1, o:321, a:1, s:1, b:1),
% 4.59/4.96 alpha43 [279, 3] (w:1, o:276, a:1, s:1, b:1),
% 4.59/4.96 alpha44 [280, 3] (w:1, o:277, a:1, s:1, b:1),
% 4.59/4.96 alpha45 [281, 3] (w:1, o:278, a:1, s:1, b:1),
% 4.59/4.96 alpha46 [282, 3] (w:1, o:279, a:1, s:1, b:1),
% 4.59/4.96 alpha47 [283, 4] (w:1, o:322, a:1, s:1, b:1),
% 4.59/4.96 alpha48 [284, 3] (w:1, o:280, a:1, s:1, b:1),
% 4.59/4.96 alpha49 [285, 4] (w:1, o:323, a:1, s:1, b:1),
% 4.59/4.96 alpha50 [286, 4] (w:1, o:300, a:1, s:1, b:1),
% 4.59/4.96 alpha51 [287, 3] (w:1, o:281, a:1, s:1, b:1),
% 4.59/4.96 alpha52 [288, 4] (w:1, o:301, a:1, s:1, b:1),
% 4.59/4.96 alpha53 [289, 4] (w:1, o:302, a:1, s:1, b:1),
% 4.59/4.96 alpha54 [290, 4] (w:1, o:303, a:1, s:1, b:1),
% 4.59/4.96 alpha55 [291, 4] (w:1, o:304, a:1, s:1, b:1),
% 4.59/4.96 alpha56 [292, 4] (w:1, o:305, a:1, s:1, b:1),
% 4.59/4.96 alpha57 [293, 3] (w:1, o:282, a:1, s:1, b:1),
% 4.59/4.96 alpha58 [294, 3] (w:1, o:283, a:1, s:1, b:1),
% 4.59/4.96 alpha59 [295, 3] (w:1, o:284, a:1, s:1, b:1),
% 4.59/4.96 alpha60 [296, 4] (w:1, o:307, a:1, s:1, b:1),
% 4.59/4.96 alpha61 [297, 3] (w:1, o:285, a:1, s:1, b:1),
% 4.59/4.96 alpha62 [298, 4] (w:1, o:308, a:1, s:1, b:1),
% 4.59/4.96 alpha63 [299, 4] (w:1, o:309, a:1, s:1, b:1),
% 4.59/4.96 skol1 [300, 2] (w:1, o:229, a:1, s:1, b:1),
% 4.59/4.96 skol2 [301, 1] (w:1, o:111, a:1, s:1, b:1),
% 4.59/4.96 skol3 [302, 0] (w:1, o:14, a:1, s:1, b:1),
% 4.59/4.96 skol4 [303, 3] (w:1, o:286, a:1, s:1, b:1),
% 4.59/4.96 skol5 [304, 1] (w:1, o:112, a:1, s:1, b:1),
% 4.59/4.96 skol6 [305, 0] (w:1, o:15, a:1, s:1, b:1),
% 4.59/4.96 skol7 [306, 3] (w:1, o:287, a:1, s:1, b:1),
% 4.59/4.96 skol8 [307, 2] (w:1, o:230, a:1, s:1, b:1),
% 33.35/33.74 skol9 [308, 2] (w:1, o:231, a:1, s:1, b:1),
% 33.35/33.74 skol10 [309, 3] (w:1, o:288, a:1, s:1, b:1),
% 33.35/33.74 skol11 [310, 4] (w:1, o:324, a:1, s:1, b:1),
% 33.35/33.74 skol12 [311, 2] (w:1, o:232, a:1, s:1, b:1),
% 33.35/33.74 skol13 [312, 1] (w:1, o:110, a:1, s:1, b:1),
% 33.35/33.74 skol14 [313, 2] (w:1, o:233, a:1, s:1, b:1),
% 33.35/33.74 skol15 [314, 3] (w:1, o:289, a:1, s:1, b:1),
% 33.35/33.74 skol16 [315, 3] (w:1, o:290, a:1, s:1, b:1),
% 33.35/33.74 skol17 [316, 2] (w:1, o:234, a:1, s:1, b:1),
% 33.35/33.74 skol18 [317, 2] (w:1, o:235, a:1, s:1, b:1),
% 33.35/33.74 skol19 [318, 3] (w:1, o:291, a:1, s:1, b:1),
% 33.35/33.74 skol20 [319, 3] (w:1, o:292, a:1, s:1, b:1),
% 33.35/33.74 skol21 [320, 3] (w:1, o:293, a:1, s:1, b:1),
% 33.35/33.74 skol22 [321, 3] (w:1, o:294, a:1, s:1, b:1),
% 33.35/33.74 skol23 [322, 1] (w:1, o:113, a:1, s:1, b:1),
% 33.35/33.74 skol24 [323, 3] (w:1, o:295, a:1, s:1, b:1),
% 33.35/33.74 skol25 [324, 3] (w:1, o:296, a:1, s:1, b:1),
% 33.35/33.74 skol26 [325, 3] (w:1, o:297, a:1, s:1, b:1),
% 33.35/33.74 skol27 [326, 3] (w:1, o:298, a:1, s:1, b:1),
% 33.35/33.74 skol28 [327, 5] (w:1, o:327, a:1, s:1, b:1).
% 33.35/33.74
% 33.35/33.74
% 33.35/33.74 Starting Search:
% 33.35/33.74
% 33.35/33.74 *** allocated 170857 integers for clauses
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74
% 33.35/33.74 Intermediate Status:
% 33.35/33.74 Generated: 2916
% 33.35/33.74 Kept: 2001
% 33.35/33.74 Inuse: 31
% 33.35/33.74 Deleted: 0
% 33.35/33.74 Deletedinuse: 0
% 33.35/33.74
% 33.35/33.74 *** allocated 256285 integers for clauses
% 33.35/33.74 *** allocated 170857 integers for termspace/termends
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74 *** allocated 384427 integers for clauses
% 33.35/33.74
% 33.35/33.74 Intermediate Status:
% 33.35/33.74 Generated: 9063
% 33.35/33.74 Kept: 4093
% 33.35/33.74 Inuse: 141
% 33.35/33.74 Deleted: 3
% 33.35/33.74 Deletedinuse: 3
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74 *** allocated 256285 integers for termspace/termends
% 33.35/33.74
% 33.35/33.74 Intermediate Status:
% 33.35/33.74 Generated: 14871
% 33.35/33.74 Kept: 6412
% 33.35/33.74 Inuse: 206
% 33.35/33.74 Deleted: 3
% 33.35/33.74 Deletedinuse: 3
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74 *** allocated 576640 integers for clauses
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74
% 33.35/33.74 Intermediate Status:
% 33.35/33.74 Generated: 19185
% 33.35/33.74 Kept: 8496
% 33.35/33.74 Inuse: 241
% 33.35/33.74 Deleted: 3
% 33.35/33.74 Deletedinuse: 3
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74 *** allocated 384427 integers for termspace/termends
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74 *** allocated 864960 integers for clauses
% 33.35/33.74
% 33.35/33.74 Intermediate Status:
% 33.35/33.74 Generated: 28501
% 33.35/33.74 Kept: 11099
% 33.35/33.74 Inuse: 288
% 33.35/33.74 Deleted: 6
% 33.35/33.74 Deletedinuse: 3
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74
% 33.35/33.74 Intermediate Status:
% 33.35/33.74 Generated: 35173
% 33.35/33.74 Kept: 13128
% 33.35/33.74 Inuse: 309
% 33.35/33.74 Deleted: 7
% 33.35/33.74 Deletedinuse: 3
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74 *** allocated 576640 integers for termspace/termends
% 33.35/33.74
% 33.35/33.74 Intermediate Status:
% 33.35/33.74 Generated: 42431
% 33.35/33.74 Kept: 15190
% 33.35/33.74 Inuse: 332
% 33.35/33.74 Deleted: 7
% 33.35/33.74 Deletedinuse: 3
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74 *** allocated 1297440 integers for clauses
% 33.35/33.74
% 33.35/33.74 Intermediate Status:
% 33.35/33.74 Generated: 50958
% 33.35/33.74 Kept: 17490
% 33.35/33.74 Inuse: 370
% 33.35/33.74 Deleted: 9
% 33.35/33.74 Deletedinuse: 3
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74
% 33.35/33.74 Intermediate Status:
% 33.35/33.74 Generated: 57043
% 33.35/33.74 Kept: 19683
% 33.35/33.74 Inuse: 409
% 33.35/33.74 Deleted: 10
% 33.35/33.74 Deletedinuse: 3
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74 Resimplifying clauses:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74 *** allocated 864960 integers for termspace/termends
% 33.35/33.74
% 33.35/33.74 Intermediate Status:
% 33.35/33.74 Generated: 63250
% 33.35/33.74 Kept: 22191
% 33.35/33.74 Inuse: 434
% 33.35/33.74 Deleted: 142
% 33.35/33.74 Deletedinuse: 3
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74
% 33.35/33.74 Intermediate Status:
% 33.35/33.74 Generated: 68846
% 33.35/33.74 Kept: 24236
% 33.35/33.74 Inuse: 475
% 33.35/33.74 Deleted: 142
% 33.35/33.74 Deletedinuse: 3
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74 *** allocated 1946160 integers for clauses
% 33.35/33.74
% 33.35/33.74 Intermediate Status:
% 33.35/33.74 Generated: 75398
% 33.35/33.74 Kept: 26237
% 33.35/33.74 Inuse: 517
% 33.35/33.74 Deleted: 142
% 33.35/33.74 Deletedinuse: 3
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74
% 33.35/33.74 Intermediate Status:
% 33.35/33.74 Generated: 80677
% 33.35/33.74 Kept: 28406
% 33.35/33.74 Inuse: 529
% 33.35/33.74 Deleted: 142
% 33.35/33.74 Deletedinuse: 3
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74
% 33.35/33.74 Intermediate Status:
% 33.35/33.74 Generated: 90578
% 33.35/33.74 Kept: 30859
% 33.35/33.74 Inuse: 549
% 33.35/33.74 Deleted: 142
% 33.35/33.74 Deletedinuse: 3
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74 Resimplifying inuse:
% 33.35/33.74 Done
% 33.35/33.74
% 33.35/33.74
% 33.35/33.74 Intermediate Status:
% 33.35/33.74 Generated: 97003
% 33.35/33.74 Kept: 32879
% 33.35/33.74 Inuse: 561
% 33.35/33.74 Deleted: 142
% 93.78/94.18 Deletedinuse: 3
% 93.78/94.18
% 93.78/94.18 *** allocated 1297440 integers for termspace/termends
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 105740
% 93.78/94.18 Kept: 35014
% 93.78/94.18 Inuse: 589
% 93.78/94.18 Deleted: 142
% 93.78/94.18 Deletedinuse: 3
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 114321
% 93.78/94.18 Kept: 37286
% 93.78/94.18 Inuse: 618
% 93.78/94.18 Deleted: 143
% 93.78/94.18 Deletedinuse: 3
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 124324
% 93.78/94.18 Kept: 39301
% 93.78/94.18 Inuse: 631
% 93.78/94.18 Deleted: 143
% 93.78/94.18 Deletedinuse: 3
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18 Resimplifying clauses:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18 *** allocated 2919240 integers for clauses
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 131505
% 93.78/94.18 Kept: 41317
% 93.78/94.18 Inuse: 648
% 93.78/94.18 Deleted: 211
% 93.78/94.18 Deletedinuse: 3
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 139185
% 93.78/94.18 Kept: 43689
% 93.78/94.18 Inuse: 663
% 93.78/94.18 Deleted: 211
% 93.78/94.18 Deletedinuse: 3
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18 *** allocated 1946160 integers for termspace/termends
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 161366
% 93.78/94.18 Kept: 45866
% 93.78/94.18 Inuse: 673
% 93.78/94.18 Deleted: 211
% 93.78/94.18 Deletedinuse: 3
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 173900
% 93.78/94.18 Kept: 48439
% 93.78/94.18 Inuse: 683
% 93.78/94.18 Deleted: 211
% 93.78/94.18 Deletedinuse: 3
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 187453
% 93.78/94.18 Kept: 50904
% 93.78/94.18 Inuse: 743
% 93.78/94.18 Deleted: 211
% 93.78/94.18 Deletedinuse: 3
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 204793
% 93.78/94.18 Kept: 53281
% 93.78/94.18 Inuse: 753
% 93.78/94.18 Deleted: 211
% 93.78/94.18 Deletedinuse: 3
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 221645
% 93.78/94.18 Kept: 56359
% 93.78/94.18 Inuse: 758
% 93.78/94.18 Deleted: 212
% 93.78/94.18 Deletedinuse: 4
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 233175
% 93.78/94.18 Kept: 60102
% 93.78/94.18 Inuse: 793
% 93.78/94.18 Deleted: 212
% 93.78/94.18 Deletedinuse: 4
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18 Resimplifying clauses:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18 *** allocated 4378860 integers for clauses
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 266650
% 93.78/94.18 Kept: 63144
% 93.78/94.18 Inuse: 813
% 93.78/94.18 Deleted: 308
% 93.78/94.18 Deletedinuse: 4
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18 *** allocated 2919240 integers for termspace/termends
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 277784
% 93.78/94.18 Kept: 65262
% 93.78/94.18 Inuse: 838
% 93.78/94.18 Deleted: 308
% 93.78/94.18 Deletedinuse: 4
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 283530
% 93.78/94.18 Kept: 67816
% 93.78/94.18 Inuse: 848
% 93.78/94.18 Deleted: 308
% 93.78/94.18 Deletedinuse: 4
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 291498
% 93.78/94.18 Kept: 70042
% 93.78/94.18 Inuse: 868
% 93.78/94.18 Deleted: 308
% 93.78/94.18 Deletedinuse: 4
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 301371
% 93.78/94.18 Kept: 72135
% 93.78/94.18 Inuse: 908
% 93.78/94.18 Deleted: 308
% 93.78/94.18 Deletedinuse: 4
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 313782
% 93.78/94.18 Kept: 75064
% 93.78/94.18 Inuse: 923
% 93.78/94.18 Deleted: 308
% 93.78/94.18 Deletedinuse: 4
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 320173
% 93.78/94.18 Kept: 77763
% 93.78/94.18 Inuse: 933
% 93.78/94.18 Deleted: 308
% 93.78/94.18 Deletedinuse: 4
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 325128
% 93.78/94.18 Kept: 80270
% 93.78/94.18 Inuse: 938
% 93.78/94.18 Deleted: 308
% 93.78/94.18 Deletedinuse: 4
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18 Resimplifying clauses:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 330150
% 93.78/94.18 Kept: 82804
% 93.78/94.18 Inuse: 943
% 93.78/94.18 Deleted: 454
% 93.78/94.18 Deletedinuse: 4
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 340780
% 93.78/94.18 Kept: 85119
% 93.78/94.18 Inuse: 958
% 93.78/94.18 Deleted: 606
% 93.78/94.18 Deletedinuse: 156
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 349413
% 93.78/94.18 Kept: 87130
% 93.78/94.18 Inuse: 991
% 93.78/94.18 Deleted: 606
% 93.78/94.18 Deletedinuse: 156
% 93.78/94.18
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 366735
% 93.78/94.18 Kept: 89208
% 93.78/94.18 Inuse: 993
% 93.78/94.18 Deleted: 606
% 93.78/94.18 Deletedinuse: 156
% 93.78/94.18
% 93.78/94.18 Resimplifying inuse:
% 93.78/94.18 Done
% 93.78/94.18
% 93.78/94.18
% 93.78/94.18 Intermediate Status:
% 93.78/94.18 Generated: 395062
% 93.78/94.18 Kept: 92131
% 93.78/94.18 Inuse: 1008
% 93.78/94.18 Deleted: 606
% 241.68/242.13 Deletedinuse: 156
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 423118
% 241.68/242.13 Kept: 94785
% 241.68/242.13 Inuse: 1018
% 241.68/242.13 Deleted: 606
% 241.68/242.13 Deletedinuse: 156
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13 *** allocated 4378860 integers for termspace/termends
% 241.68/242.13 *** allocated 6568290 integers for clauses
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 434998
% 241.68/242.13 Kept: 97534
% 241.68/242.13 Inuse: 1028
% 241.68/242.13 Deleted: 606
% 241.68/242.13 Deletedinuse: 156
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 446021
% 241.68/242.13 Kept: 100099
% 241.68/242.13 Inuse: 1038
% 241.68/242.13 Deleted: 606
% 241.68/242.13 Deletedinuse: 156
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13 Resimplifying clauses:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 457212
% 241.68/242.13 Kept: 102106
% 241.68/242.13 Inuse: 1074
% 241.68/242.13 Deleted: 4364
% 241.68/242.13 Deletedinuse: 156
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 471685
% 241.68/242.13 Kept: 105327
% 241.68/242.13 Inuse: 1108
% 241.68/242.13 Deleted: 4364
% 241.68/242.13 Deletedinuse: 156
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 484503
% 241.68/242.13 Kept: 108642
% 241.68/242.13 Inuse: 1123
% 241.68/242.13 Deleted: 4365
% 241.68/242.13 Deletedinuse: 157
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 489597
% 241.68/242.13 Kept: 111011
% 241.68/242.13 Inuse: 1128
% 241.68/242.13 Deleted: 4365
% 241.68/242.13 Deletedinuse: 157
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 500526
% 241.68/242.13 Kept: 113456
% 241.68/242.13 Inuse: 1138
% 241.68/242.13 Deleted: 4365
% 241.68/242.13 Deletedinuse: 157
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 509129
% 241.68/242.13 Kept: 118043
% 241.68/242.13 Inuse: 1143
% 241.68/242.13 Deleted: 4365
% 241.68/242.13 Deletedinuse: 157
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 519296
% 241.68/242.13 Kept: 123191
% 241.68/242.13 Inuse: 1168
% 241.68/242.13 Deleted: 4365
% 241.68/242.13 Deletedinuse: 157
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13 Resimplifying clauses:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 536416
% 241.68/242.13 Kept: 127005
% 241.68/242.13 Inuse: 1198
% 241.68/242.13 Deleted: 5603
% 241.68/242.13 Deletedinuse: 160
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 546702
% 241.68/242.13 Kept: 129042
% 241.68/242.13 Inuse: 1229
% 241.68/242.13 Deleted: 5603
% 241.68/242.13 Deletedinuse: 160
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 556377
% 241.68/242.13 Kept: 131168
% 241.68/242.13 Inuse: 1253
% 241.68/242.13 Deleted: 5603
% 241.68/242.13 Deletedinuse: 160
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 577977
% 241.68/242.13 Kept: 133179
% 241.68/242.13 Inuse: 1297
% 241.68/242.13 Deleted: 5603
% 241.68/242.13 Deletedinuse: 160
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 591583
% 241.68/242.13 Kept: 135184
% 241.68/242.13 Inuse: 1307
% 241.68/242.13 Deleted: 5603
% 241.68/242.13 Deletedinuse: 160
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 601062
% 241.68/242.13 Kept: 138537
% 241.68/242.13 Inuse: 1318
% 241.68/242.13 Deleted: 5603
% 241.68/242.13 Deletedinuse: 160
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 607468
% 241.68/242.13 Kept: 141103
% 241.68/242.13 Inuse: 1323
% 241.68/242.13 Deleted: 5603
% 241.68/242.13 Deletedinuse: 160
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 618127
% 241.68/242.13 Kept: 143118
% 241.68/242.13 Inuse: 1349
% 241.68/242.13 Deleted: 5604
% 241.68/242.13 Deletedinuse: 160
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13 Resimplifying clauses:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 627975
% 241.68/242.13 Kept: 145210
% 241.68/242.13 Inuse: 1357
% 241.68/242.13 Deleted: 5993
% 241.68/242.13 Deletedinuse: 160
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13 *** allocated 9852435 integers for clauses
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 638245
% 241.68/242.13 Kept: 147584
% 241.68/242.13 Inuse: 1377
% 241.68/242.13 Deleted: 5994
% 241.68/242.13 Deletedinuse: 161
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 648169
% 241.68/242.13 Kept: 149603
% 241.68/242.13 Inuse: 1397
% 241.68/242.13 Deleted: 5994
% 241.68/242.13 Deletedinuse: 161
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 655664
% 241.68/242.13 Kept: 152786
% 241.68/242.13 Inuse: 1407
% 241.68/242.13 Deleted: 5994
% 241.68/242.13 Deletedinuse: 161
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 660218
% 241.68/242.13 Kept: 154876
% 241.68/242.13 Inuse: 1412
% 241.68/242.13 Deleted: 5994
% 241.68/242.13 Deletedinuse: 161
% 241.68/242.13
% 241.68/242.13 Resimplifying inuse:
% 241.68/242.13 Done
% 241.68/242.13
% 241.68/242.13
% 241.68/242.13 Intermediate Status:
% 241.68/242.13 Generated: 666112
% 241.68/242.13 Kept: 157146
% 241.68/242.13 Inuse: 1422
% 241.68/242.13 Deleted: 5994
% 241.68/242.13 Deletedinuse: 161
% 241.68/242.13
% 241.68/242.13 Resimplifying inusCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------