TSTP Solution File: SWW287+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW287+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n032.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 23:21:51 EDT 2022
% Result : Timeout 300.11s 300.59s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : SWW287+1 : TPTP v8.1.0. Released v5.2.0.
% 0.02/0.09 % Command : bliksem %s
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % DateTime : Sun Jun 5 21:37:19 EDT 2022
% 0.08/0.28 % CPUTime :
% 0.75/1.37 *** allocated 10000 integers for termspace/termends
% 0.75/1.37 *** allocated 10000 integers for clauses
% 0.75/1.37 *** allocated 10000 integers for justifications
% 0.75/1.37 *** allocated 15000 integers for termspace/termends
% 0.75/1.37 *** allocated 22500 integers for termspace/termends
% 0.75/1.37 *** allocated 33750 integers for termspace/termends
% 0.75/1.37 Bliksem 1.12
% 0.75/1.37
% 0.75/1.37
% 0.75/1.37 Automatic Strategy Selection
% 0.75/1.37
% 0.75/1.37 *** allocated 50625 integers for termspace/termends
% 0.75/1.37 *** allocated 75937 integers for termspace/termends
% 0.75/1.37 *** allocated 113905 integers for termspace/termends
% 0.75/1.37
% 0.75/1.37 Clauses:
% 0.75/1.37
% 0.75/1.37 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.75/1.37 { ! v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.75/1.37 tc_Complex_Ocomplex ) ) }.
% 0.75/1.37 { ! c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.37 { c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) = c_Nat_OSuc( v_n____ )
% 0.75/1.37 }.
% 0.75/1.37 { ! v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.75/1.37 tc_Complex_Ocomplex ) ), ! alpha1, hBOOL( hAPP( hAPP(
% 0.75/1.37 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ),
% 0.75/1.37 v_p ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.75/1.37 tc_Complex_Ocomplex ) ), v_q ), c_Polynomial_Odegree( tc_Complex_Ocomplex
% 0.75/1.37 , v_p ) ) ) ), alpha28 }.
% 0.75/1.37 { ! v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.75/1.37 tc_Complex_Ocomplex ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.37 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), v_p ), hAPP( hAPP(
% 0.75/1.37 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.75/1.37 ), v_q ), c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) ) ) ), alpha1
% 0.75/1.37 }.
% 0.75/1.37 { ! v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.75/1.37 tc_Complex_Ocomplex ) ), ! alpha28, alpha1 }.
% 0.75/1.37 { ! alpha28, v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.75/1.37 tc_Complex_Ocomplex ) ) }.
% 0.75/1.37 { ! alpha28, v_q = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.75/1.37 tc_Complex_Ocomplex ) ) }.
% 0.75/1.37 { ! v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.75/1.37 tc_Complex_Ocomplex ) ), ! v_q = c_Groups_Ozero__class_Ozero(
% 0.75/1.37 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), alpha28 }.
% 0.75/1.37 { ! alpha1, ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), X ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.75/1.37 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q ), X ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.75/1.37 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), skol2 ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), alpha1 }.
% 0.75/1.37 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q ), skol2 ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), alpha1 }.
% 0.75/1.37 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.75/1.37 tc_Complex_Ocomplex ) ), v_p ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.75/1.37 ( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), v_q ), c_Nat_OSuc(
% 0.75/1.37 v_n____ ) ) ) ), ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ),
% 0.75/1.37 X ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.75/1.37 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q ), X ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.75/1.37 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), skol3 ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), c_Polynomial_Odegree
% 0.75/1.37 ( tc_Complex_Ocomplex, v_p ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.75/1.37 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.75/1.37 tc_Complex_Ocomplex ) ), v_p ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.75/1.37 ( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), v_q ),
% 0.75/1.37 c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) ) ) ) }.
% 0.75/1.37 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q ), skol3 ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), c_Polynomial_Odegree
% 0.75/1.37 ( tc_Complex_Ocomplex, v_p ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.75/1.37 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.75/1.37 tc_Complex_Ocomplex ) ), v_p ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.75/1.37 ( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), v_q ),
% 0.75/1.37 c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) ) ) ) }.
% 0.75/1.37 { ! c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! alpha2, hBOOL( hAPP( hAPP(
% 0.75/1.37 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ),
% 0.75/1.37 v_p ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.75/1.37 tc_Complex_Ocomplex ) ), v_q ), c_Polynomial_Odegree( tc_Complex_Ocomplex
% 0.75/1.37 , v_p ) ) ) ), alpha29 }.
% 0.75/1.37 { ! c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.75/1.37 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ),
% 0.75/1.37 v_p ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.75/1.37 tc_Complex_Ocomplex ) ), v_q ), c_Polynomial_Odegree( tc_Complex_Ocomplex
% 0.75/1.37 , v_p ) ) ) ), alpha2 }.
% 0.75/1.37 { ! c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! alpha29, alpha2 }.
% 0.75/1.37 { ! alpha29, v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.75/1.37 tc_Complex_Ocomplex ) ) }.
% 0.75/1.37 { ! alpha29, v_q = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.75/1.37 tc_Complex_Ocomplex ) ) }.
% 0.75/1.37 { ! v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.75/1.37 tc_Complex_Ocomplex ) ), ! v_q = c_Groups_Ozero__class_Ozero(
% 0.75/1.37 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), alpha29 }.
% 0.75/1.37 { ! alpha2, ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), X ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.75/1.37 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q ), X ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.75/1.37 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), skol4 ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), alpha2 }.
% 0.75/1.37 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q ), skol4 ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), alpha2 }.
% 0.75/1.37 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.75/1.37 c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) )
% 0.75/1.37 }.
% 0.75/1.37 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.75/1.37 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.75/1.37 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.75/1.37 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.75/1.37 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.37 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.75/1.37 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.37 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.75/1.37 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.75/1.37 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.75/1.37 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.75/1.37 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.75/1.37 X ), Z ), T ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T )
% 0.75/1.37 ) ) }.
% 0.75/1.37 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.75/1.37 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.75/1.37 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.75/1.37 .
% 0.75/1.37 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.75/1.37 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.75/1.37 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.37 tc_Nat_Onat ) }.
% 0.75/1.37 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.75/1.37 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.75/1.37 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.75/1.37 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.75/1.37 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.37 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.75/1.37 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.75/1.37 ( X ) }.
% 0.75/1.37 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.75/1.37 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) )
% 0.75/1.37 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.37 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), skol5( Z, Y ) ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.75/1.37 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = T, T =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.75/1.37 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), Y
% 0.75/1.37 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.75/1.37 tc_Complex_Ocomplex ) ), X ), T ) ) ) }.
% 0.75/1.37 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol5( X, Y ) ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.75/1.37 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = Z, Z =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.75/1.37 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), Y
% 0.75/1.37 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.75/1.37 tc_Complex_Ocomplex ) ), X ), Z ) ) ) }.
% 0.75/1.37 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.75/1.37 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.37 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.75/1.37 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.37 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.75/1.37 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.37 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.75/1.37 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.75/1.37 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.75/1.37 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.75/1.37 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.75/1.37 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.75/1.37 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.75/1.37 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.75/1.37 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.75/1.37 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.75/1.37 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.37 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.37 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.75/1.37 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.75/1.37 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 0.75/1.37 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 0.75/1.37 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.75/1.37 c_Rings_Odvd__class_Odvd( X ), Y ), Y ) ) }.
% 0.75/1.37 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.75/1.37 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.75/1.37 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.75/1.37 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.75/1.37 { c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) = c_Nat_OSuc( skol6 ) }
% 0.75/1.37 .
% 0.75/1.37 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), c_Nat_OSuc(
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 0.75/1.37 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.37 tc_Polynomial_Opoly( X ) ),
% 0.75/1.37 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.37 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.37 tc_Polynomial_Opoly( X ) ),
% 0.75/1.37 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 0.75/1.37 c_Polynomial_Odegree( X, Y ) ) }.
% 0.75/1.37 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.75/1.37 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.75/1.37 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.37 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.37 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.75/1.37 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.75/1.37 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.75/1.37 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hBOOL(
% 0.75/1.37 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Nat_OSuc(
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.75/1.37 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.75/1.37 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.37 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 0.75/1.37 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.75/1.37 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.75/1.37 }.
% 0.75/1.37 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 0.75/1.37 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 0.75/1.37 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.37 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), X ) ) }
% 0.75/1.37 .
% 0.75/1.37 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.75/1.37 , X ) ) }.
% 0.75/1.37 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X )
% 0.75/1.37 , Y ) ) }.
% 0.75/1.37 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.37 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.75/1.37 ), Y = X }.
% 0.75/1.37 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.37 , alpha3( X, Y ), Y = X }.
% 0.75/1.37 { ! alpha3( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.37 tc_Nat_Onat ), Y ), X ) ) }.
% 0.75/1.37 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.75/1.37 , X ) ) }.
% 0.75/1.37 { ! alpha3( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.37 tc_Nat_Onat ), Y ), X ) ) }.
% 0.75/1.37 { ! alpha3( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.37 tc_Nat_Onat ), X ), Y ) ) }.
% 0.75/1.37 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.37 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.75/1.37 , alpha3( X, Y ) }.
% 0.75/1.37 { ! alpha4( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.37 tc_Nat_Onat ), Y ), X ) ) }.
% 0.75/1.37 { ! alpha4( X, Y ), ! Y = X }.
% 0.75/1.37 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.37 , Y = X, alpha4( X, Y ) }.
% 0.75/1.37 { ! alpha4( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.37 tc_Nat_Onat ), Y ), X ) ) }.
% 0.75/1.37 { ! alpha4( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.37 tc_Nat_Onat ), X ), Y ) ) }.
% 0.75/1.37 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.37 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.75/1.37 , alpha4( X, Y ) }.
% 0.75/1.37 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.75/1.37 , X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.75/1.37 , X ) ) }.
% 0.75/1.37 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.75/1.37 , X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.75/1.37 ), Y ) ) }.
% 0.75/1.37 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.75/1.37 , X ) ) }.
% 0.75/1.37 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.37 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.75/1.37 ), X = Y }.
% 0.75/1.37 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.37 , ! X = Y, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.75/1.37 ), Y ) ) }.
% 0.75/1.37 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.37 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.37 , Y = X }.
% 0.75/1.37 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.37 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.75/1.38 ), Y = X }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.75/1.38 , X ) ) }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.75/1.38 ), Y ) ) }.
% 0.75/1.38 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.75/1.38 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.75/1.38 ), Z ) ) }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.75/1.38 ), Z ) ) }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.75/1.38 ), Y = X }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.75/1.38 ), Y = X }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.75/1.38 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.75/1.38 ) }.
% 0.75/1.38 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.75/1.38 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.75/1.38 ), X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.75/1.38 ), Z ) ) }.
% 0.75/1.38 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.75/1.38 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.75/1.38 ), X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.75/1.38 Z ), Y ) ) }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.75/1.38 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.75/1.38 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.75/1.38 ) }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.75/1.38 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.75/1.38 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.75/1.38 ) ) }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.75/1.38 , ! Y = X }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.75/1.38 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.75/1.38 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.75/1.38 ) }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.75/1.38 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.75/1.38 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.75/1.38 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.75/1.38 ) }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.75/1.38 , ! Y = X }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.75/1.38 , ! X = Y }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.75/1.38 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.75/1.38 ), Z ) ) }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.75/1.38 , ! X = Z, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.75/1.38 Z ), Y ) ) }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.75/1.38 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.75/1.38 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.75/1.38 ) }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.75/1.38 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.75/1.38 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.75/1.38 ) ) }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.75/1.38 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.75/1.38 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.75/1.38 ) }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.75/1.38 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.75/1.38 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.75/1.38 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.75/1.38 ) }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.75/1.38 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.75/1.38 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.75/1.38 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.75/1.38 ) ) }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.75/1.38 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.75/1.38 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.38 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.75/1.38 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.75/1.38 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.75/1.38 { ! c_Nat_OSuc( X ) = X }.
% 0.75/1.38 { ! X = c_Nat_OSuc( X ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), !
% 0.75/1.38 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ),
% 0.75/1.38 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.75/1.38 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ), Y =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 0.75/1.38 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.75/1.38 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.75/1.38 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.75/1.38 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.75/1.38 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.75/1.38 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.75/1.38 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.75/1.38 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), Z ), Y ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.75/1.38 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.75/1.38 }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 0.75/1.38 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ), Y =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ) }.
% 0.75/1.38 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ), hBOOL( hAPP(
% 0.75/1.38 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.75/1.38 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ) }.
% 0.75/1.38 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.75/1.38 ( tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, T, Z ) ), Y ) ),
% 0.75/1.38 alpha5( X, Y, T ) }.
% 0.75/1.38 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.75/1.38 ( tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, T, Z ) ), Y ) ),
% 0.75/1.38 alpha30( X, Y, Z, T ) }.
% 0.75/1.38 { ! class_Fields_Ofield( X ), ! alpha5( X, Y, T ), ! alpha30( X, Y, Z, T )
% 0.75/1.38 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.75/1.38 , c_Polynomial_Osmult( X, T, Z ) ), Y ) ) }.
% 0.75/1.38 { ! alpha30( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.75/1.38 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.75/1.38 ) ) }.
% 0.75/1.38 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha30( X, Y, Z, T ) }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.75/1.38 , Z ), Y ) ), alpha30( X, Y, Z, T ) }.
% 0.75/1.38 { ! alpha5( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.38 { Z = c_Groups_Ozero__class_Ozero( X ), alpha5( X, Y, Z ) }.
% 0.75/1.38 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha5( X
% 0.75/1.38 , Y, Z ) }.
% 0.75/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.75/1.38 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.75/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.75/1.38 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.75/1.38 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.75/1.38 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 0.75/1.38 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.75/1.38 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) )
% 0.75/1.38 , c_Polynomial_Odegree( X, Y ) ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.75/1.38 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.75/1.38 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.75/1.38 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.75/1.38 , c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Z, Y ) ), c_Nat_OSuc(
% 0.75/1.38 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.75/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.38 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.75/1.38 .
% 0.75/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.75/1.38 ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.75/1.38 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.75/1.38 , c_Nat_OSuc( X ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.75/1.38 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.75/1.38 }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.75/1.38 c_Nat_OSuc( X ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.75/1.38 ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.75/1.38 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.75/1.38 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult
% 0.75/1.38 ( X, T, Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), hBOOL(
% 0.75/1.38 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ),
% 0.75/1.38 c_Polynomial_Osmult( X, T, Y ) ) ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.75/1.38 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.75/1.38 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.75/1.38 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.38 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.75/1.38 X ), T ), Z ) ), Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.75/1.38 , U, Z ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), T ), U ) ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ), hBOOL( hAPP( hAPP
% 0.75/1.38 ( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.75/1.38 ( X ), Z ), U ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T
% 0.75/1.38 ) ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP
% 0.75/1.38 ( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.75/1.38 ( X ), T ), Z ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y
% 0.75/1.38 ) ) ) }.
% 0.75/1.38 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.75/1.38 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Osmult( X, Z, Y ) ) ), Z
% 0.75/1.38 = c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 0.75/1.38 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.75/1.38 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), T = c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.75/1.38 X ) ), c_Polynomial_Osmult( X, T, Z ) ), Y ) ) }.
% 0.75/1.38 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 0.75/1.38 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 0.75/1.38 c_Polynomial_Osmult( X, Y, Z ) ) ), hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Z ) ) }.
% 0.75/1.38 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 0.75/1.38 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 0.75/1.38 Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.75/1.38 X ) ), T ), c_Polynomial_Osmult( X, Y, Z ) ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.75/1.38 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.75/1.38 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 0.75/1.38 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.75/1.38 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 X ), Y ), Z = Y }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.38 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.38 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.75/1.38 c_Polynomial_Odegree( X, Y ) }.
% 0.75/1.38 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.75/1.38 , Y ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Omono( tc_Nat_Onat, X
% 0.75/1.38 , c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), ! hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), T ), Z ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.75/1.38 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 0.75/1.38 }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.75/1.38 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 0.75/1.38 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 0.75/1.38 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 0.75/1.38 , Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 0.75/1.38 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.75/1.38 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.75/1.38 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.75/1.38 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.75/1.38 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 0.75/1.38 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.75/1.38 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 0.75/1.38 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.38 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.75/1.38 X ) ) }.
% 0.75/1.38 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.75/1.38 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.75/1.38 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.75/1.38 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.75/1.38 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.38 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.75/1.38 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.75/1.38 .
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.75/1.38 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.75/1.38 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.75/1.38 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.75/1.38 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.75/1.38 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.75/1.38 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.75/1.38 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.75/1.38 X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.75/1.38 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.75/1.38 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.75/1.38 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.75/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.75/1.38 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.75/1.38 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.75/1.38 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.75/1.38 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.75/1.38 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.75/1.38 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.75/1.38 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.75/1.38 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.75/1.38 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.75/1.38 , ! Y = Z }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.75/1.38 , ! Z = Y }.
% 0.75/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.75/1.38 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.75/1.38 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.75/1.38 , ! Z = Y }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.75/1.38 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.75/1.38 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.75/1.38 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.75/1.38 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.75/1.38 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.75/1.38 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.75/1.38 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.75/1.38 Y ), ! Z = Y }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.75/1.38 Z ), ! Z = Y }.
% 0.75/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.75/1.38 Y ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.75/1.38 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.75/1.38 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.75/1.38 { alpha65( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.75/1.38 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.75/1.38 { alpha65( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.75/1.38 ( X, Y ), Z ) ) }.
% 0.75/1.38 { ! alpha65( X, Y, Z ), alpha67( X, Y, Z ), Z = Y }.
% 0.75/1.38 { ! alpha65( X, Y, Z ), alpha67( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.75/1.38 ) ) }.
% 0.75/1.38 { ! alpha67( X, Y, Z ), alpha65( X, Y, Z ) }.
% 0.75/1.38 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha65( X, Y, Z ) }.
% 0.75/1.38 { ! alpha67( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.75/1.38 }.
% 0.75/1.38 { ! alpha67( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.75/1.38 X, Y ), Z ) ), alpha67( X, Y, Z ) }.
% 0.75/1.38 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.75/1.38 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.75/1.38 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.38 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.75/1.38 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.75/1.38 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.38 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.75/1.38 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.75/1.38 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.38 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.75/1.38 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.75/1.38 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 0.75/1.38 .
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.75/1.38 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.75/1.38 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.75/1.38 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.75/1.38 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.75/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.38 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.75/1.38 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.75/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.75/1.38 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.75/1.38 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.75/1.38 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.75/1.38 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.38 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.38 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.75/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.75/1.38 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.38 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.75/1.38 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.75/1.38 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.75/1.38 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.75/1.38 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.75/1.38 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.75/1.38 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.75/1.38 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.75/1.38 ( X, Z, Y ) }.
% 0.75/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.75/1.38 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.75/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.75/1.38 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.38 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.75/1.38 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.75/1.38 , ! Z = Y }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.75/1.38 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.75/1.38 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.75/1.38 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.75/1.38 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.75/1.38 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.38 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.75/1.38 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.75/1.38 c_Groups_Oone__class_Oone( X ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.75/1.38 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.38 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.75/1.38 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.75/1.38 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 0.75/1.38 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.75/1.38 , Y ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.75/1.38 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.75/1.38 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) ) }.
% 0.75/1.38 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.75/1.38 c_Groups_Oone__class_Oone( X ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X, Y, T
% 0.75/1.38 ) ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), c_Groups_Oone__class_Oone( X ) ), Y ) ) }
% 0.75/1.38 .
% 0.75/1.38 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.75/1.38 = c_Groups_Oone__class_Oone( X ) }.
% 0.75/1.38 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Nat_Onat ), X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.75/1.38 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Nat_Onat ), X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.75/1.38 .
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.75/1.38 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.75/1.38 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.75/1.38 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.75/1.38 .
% 0.75/1.38 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.75/1.38 .
% 0.75/1.38 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.75/1.38 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.75/1.38 X ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.75/1.38 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.75/1.38 }.
% 0.75/1.38 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.75/1.38 tc_Nat_Onat ) ) = Y }.
% 0.75/1.38 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.75/1.38 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.75/1.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X =
% 0.75/1.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.75/1.38 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone(
% 0.75/1.38 tc_Nat_Onat ) ) ) }.
% 0.75/1.38 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.75/1.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 0.75/1.38 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 0.75/1.38 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.75/1.38 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.75/1.38 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 0.75/1.38 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 0.75/1.38 c_Polynomial_OpCons( X, T,
% 0.75/1.38 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 0.75/1.38 .
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.75/1.38 c_Groups_Oone__class_Oone( X ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), hBOOL( hAPP
% 0.75/1.38 ( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.75/1.38 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.75/1.38 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ) ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.75/1.38 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.38 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.38 c_Groups_Oone__class_Oone( X ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.75/1.38 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.75/1.38 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.75/1.38 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.75/1.38 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.75/1.38 c_Groups_Oone__class_Oone( X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha6( X, Y ) }.
% 0.75/1.38 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.75/1.38 { ! alpha6( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.75/1.38 c_Nat_OSuc( X ) ) }.
% 0.75/1.38 { ! alpha6( X, Y ), Y = c_Nat_OSuc( skol7( Z, Y ) ) }.
% 0.75/1.38 { ! alpha6( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol7( X, Y
% 0.75/1.38 ), X ) }.
% 0.75/1.38 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.75/1.38 ), alpha6( X, Y ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.38 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol8( X ) ) }.
% 0.75/1.38 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.75/1.38 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X
% 0.75/1.38 ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.38 tc_Nat_Onat ), Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.75/1.38 .
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! class_Groups_Ocomm__monoid__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.75/1.38 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.38 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 0.75/1.38 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 0.75/1.38 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 0.75/1.38 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.75/1.38 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.75/1.38 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.75/1.38 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.75/1.38 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.75/1.38 ), X ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.75/1.38 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), !
% 0.75/1.38 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( tc_Polynomial_Opoly( X ) ),
% 0.75/1.38 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.75/1.38 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) =
% 0.75/1.38 c_Polynomial_Odegree( X, Z ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.38 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.38 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.75/1.38 , c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Z, Y ) ), Y ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.75/1.38 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.75/1.38 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.75/1.38 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.75/1.38 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.75/1.38 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.75/1.38 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.75/1.38 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.75/1.38 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.75/1.38 hAPP( Y, U ) ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.75/1.38 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.75/1.38 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.75/1.38 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.38 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.75/1.38 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.75/1.38 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.75/1.38 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.75/1.38 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.75/1.38 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.75/1.38 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.75/1.38 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.75/1.38 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.75/1.38 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.75/1.38 hAPP( Y, U ) ) }.
% 0.75/1.38 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.75/1.38 ( X, Z, Y ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.75/1.38 ( X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.75/1.38 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.75/1.38 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.75/1.38 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.75/1.38 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.75/1.38 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.75/1.38 hAPP( Y, U ) ) }.
% 0.75/1.38 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.75/1.38 ( Z, skol9( X, Y, Z ) ), hAPP( Y, skol9( X, Y, Z ) ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.75/1.38 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.75/1.38 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.75/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.75/1.38 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.75/1.38 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.75/1.38 ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.75/1.38 ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.75/1.38 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.75/1.38 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.75/1.38 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.75/1.38 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.75/1.38 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.75/1.38 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Nat_Onat ), Y ) }.
% 0.75/1.38 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.75/1.38 ), X ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.75/1.38 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.75/1.38 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.75/1.38 .
% 0.75/1.38 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.75/1.38 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.75/1.38 }.
% 0.75/1.38 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.75/1.38 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.75/1.38 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.75/1.38 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Nat_Onat ), X ) = X }.
% 0.75/1.38 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( tc_Nat_Onat ) ) = X }.
% 0.75/1.38 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.38 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.38 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.38 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.38 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.75/1.38 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.75/1.38 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.75/1.38 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.75/1.38 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.75/1.38 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.75/1.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.75/1.38 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.75/1.38 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.75/1.38 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.75/1.38 , X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.75/1.38 .
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.75/1.38 .
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.75/1.38 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.75/1.38 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.75/1.38 .
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.75/1.38 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.75/1.38 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ), hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.38 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol10( X, Y ) ) }.
% 0.75/1.38 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.75/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.75/1.38 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha7( X, Y ), alpha31
% 0.75/1.38 ( X, Y ) }.
% 0.75/1.38 { ! alpha7( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.75/1.38 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! alpha31( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.75/1.38 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! alpha31( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.38 { ! alpha31( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Nat_Onat ) ) }.
% 0.75/1.38 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha31( X, Y ) }.
% 0.75/1.38 { ! alpha7( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Nat_Onat ) ) }.
% 0.75/1.38 { ! alpha7( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.38 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha7( X, Y ) }.
% 0.75/1.38 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha8( X, Y ), alpha32( X
% 0.75/1.38 , Y ) }.
% 0.75/1.38 { ! alpha8( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.75/1.38 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.75/1.38 { ! alpha32( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.75/1.38 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.75/1.38 { ! alpha32( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.38 { ! alpha32( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Nat_Onat ) ) }.
% 0.75/1.38 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha32( X, Y ) }.
% 0.75/1.38 { ! alpha8( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Nat_Onat ) ) }.
% 0.75/1.38 { ! alpha8( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.38 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Nat_Onat, Y, X ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Nat_Onat, Y, X ) ) }.
% 0.75/1.38 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.75/1.38 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol11( X, Y ) ) ) }.
% 0.75/1.38 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.75/1.38 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.75/1.38 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.75/1.38 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 T, Y ), Z = Y }.
% 0.75/1.38 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 T, Y ) }.
% 0.75/1.38 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 Y, Z ), T = Y }.
% 0.75/1.38 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 Y, Z ) }.
% 0.75/1.38 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 T, Y ), Z = Y }.
% 0.75/1.38 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 T, Y ), Z = Y }.
% 0.75/1.38 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 Y, T ), Z = Y }.
% 0.75/1.38 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.75/1.38 c_Groups_Oone__class_Oone( X ) }.
% 0.75/1.38 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.75/1.38 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.75/1.38 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.75/1.38 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.75/1.38 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.75/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.75/1.38 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.75/1.38 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.75/1.38 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.75/1.38 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.75/1.38 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.75/1.38 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.75/1.38 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.75/1.38 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.75/1.38 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.75/1.38 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.75/1.38 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.75/1.38 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.75/1.38 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, T, Y ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.75/1.38 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.75/1.38 , Y, Z ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.75/1.38 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, Z, Y ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.75/1.38 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.75/1.38 , T, Y ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.75/1.38 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.75/1.38 , Y, T ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.75/1.38 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.75/1.38 , T, Y ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.75/1.38 , T ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.75/1.38 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, Z, Y ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.75/1.38 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, Z, Y ) }.
% 0.75/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.38 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.75/1.38 ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 Z, Y ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 Y, Z ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.75/1.38 .
% 0.75/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.75/1.38 .
% 0.75/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.75/1.38 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.75/1.38 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.75/1.38 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.75/1.38 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.75/1.38 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.75/1.38 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.75/1.38 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.75/1.38 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.75/1.38 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.75/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.75/1.38 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.75/1.38 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.75/1.38 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.75/1.38 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.75/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.75/1.38 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.75/1.38 , Y, T ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.75/1.38 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.75/1.38 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.75/1.38 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.75/1.38 ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.75/1.38 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.75/1.38 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.75/1.38 ) ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.75/1.38 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Oorder( X, Z, Y ) ) ), Y )
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.75/1.38 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.75/1.38 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.75/1.38 Y ) ) ) ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.75/1.38 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.75/1.38 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.75/1.38 Y ) ) ) ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.75/1.38 tc_Nat_Onat ) ) = Y }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.75/1.38 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.75/1.38 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.75/1.38 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.75/1.38 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.75/1.38 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.75/1.38 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.75/1.38 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.75/1.38 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.75/1.38 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.75/1.38 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.75/1.38 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.75/1.38 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.75/1.38 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.75/1.38 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.75/1.38 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.75/1.38 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.75/1.38 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.75/1.38 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.75/1.38 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.75/1.38 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.75/1.38 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.75/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.75/1.38 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.75/1.38 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.75/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.75/1.38 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.75/1.38 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.75/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.75/1.38 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.75/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.75/1.38 = Y }.
% 0.75/1.38 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.75/1.38 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( X ) }.
% 0.75/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.75/1.38 , Y ) }.
% 0.75/1.38 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 = Y }.
% 0.75/1.38 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.75/1.38 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.75/1.38 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.75/1.38 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.75/1.38 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.75/1.38 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.75/1.38 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.75/1.38 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.75/1.38 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.75/1.38 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.75/1.38 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.75/1.38 ( X, Y ), Z ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.75/1.38 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.75/1.38 ( X, Z ), Y ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.75/1.38 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.75/1.38 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.75/1.38 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.75/1.38 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.75/1.38 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.75/1.38 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.75/1.38 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.75/1.38 Y ) ) = Y }.
% 0.75/1.38 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 Z, Y ) ) = Y }.
% 0.75/1.38 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.75/1.38 ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.75/1.38 ) ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ouminus__class_Ouminus( X, Z ) )
% 0.75/1.38 , Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ouminus__class_Ouminus( X, Z ) )
% 0.75/1.38 , Y ) ) }.
% 0.75/1.38 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.75/1.38 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.38 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.75/1.38 c_Polynomial_Odegree( X, Y ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.75/1.38 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.75/1.38 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.75/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.75/1.38 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.75/1.38 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.75/1.38 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.75/1.38 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.75/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.75/1.38 ( X, Y ), Y ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.75/1.38 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.75/1.38 .
% 0.75/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.75/1.38 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.75/1.38 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.75/1.38 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.75/1.38 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.75/1.38 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.75/1.38 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 , Y ) }.
% 0.75/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.75/1.38 , Y ) }.
% 0.75/1.38 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 X ) }.
% 0.75/1.38 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.75/1.38 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.75/1.38 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.75/1.38 ( X, Y ) }.
% 0.75/1.38 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.75/1.38 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.75/1.38 ( X, Z ) }.
% 0.75/1.38 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.75/1.38 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.75/1.38 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.75/1.38 Z ) = Y }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.75/1.38 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.75/1.38 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.75/1.38 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.75/1.38 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.75/1.38 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.75/1.38 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.75/1.38 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.75/1.38 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.75/1.38 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.75/1.38 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.75/1.38 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.75/1.38 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.75/1.38 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.75/1.38 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.75/1.38 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), ! hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP( hAPP
% 0.75/1.38 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ), X = Y }.
% 0.75/1.38 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.75/1.38 , ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.75/1.38 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X
% 0.75/1.38 ) ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons
% 0.75/1.38 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.75/1.38 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.75/1.38 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.75/1.38 , Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X, Z,
% 0.75/1.38 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ),
% 0.75/1.38 hAPP( c_Polynomial_Opoly( X, Y ), c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.75/1.38 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.75/1.38 ) ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.75/1.38 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.75/1.38 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.75/1.38 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.75/1.38 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.75/1.38 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.75/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.75/1.38 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.75/1.38 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Oorder( X, Z, Y ) ) ), Y )
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.75/1.38 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.75/1.38 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol12( X, Y ) ) }.
% 0.75/1.38 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.75/1.38 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ), alpha9
% 0.75/1.38 ( X, Y, Z ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.75/1.38 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__idom( X ), ! alpha9( X, Y, Z ),
% 0.75/1.38 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.75/1.38 { ! alpha9( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 0.75/1.38 ( X ) ) }.
% 0.75/1.38 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.75/1.38 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.75/1.38 alpha9( X, Y, Z ) }.
% 0.75/1.38 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.75/1.38 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.75/1.38 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.75/1.38 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.75/1.38 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.75/1.38 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.75/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.75/1.38 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.75/1.38 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.75/1.38 }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.75/1.38 tc_Int_Oint ) ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.75/1.38 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.75/1.38 }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.75/1.38 tc_Int_Oint ) ), X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.75/1.38 tc_Int_Oint ) ), X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.75/1.38 .
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.75/1.38 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.38 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Int_Oint ), X ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.38 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.75/1.38 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.75/1.38 ( tc_Int_Oint ) }.
% 0.75/1.38 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.75/1.38 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.75/1.38 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Int_Oint ), X ) = X }.
% 0.75/1.38 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( tc_Int_Oint ) ) = X }.
% 0.75/1.38 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.75/1.38 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.75/1.38 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.75/1.38 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.75/1.38 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.75/1.38 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.75/1.38 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.75/1.38 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.75/1.38 .
% 0.75/1.38 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.75/1.38 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.38 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.75/1.38 ), U = Z, T = Y }.
% 0.75/1.38 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.75/1.38 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.38 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.75/1.38 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.38 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.75/1.38 ) ), Z ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.75/1.38 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.75/1.38 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.75/1.38 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.38 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.75/1.38 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.38 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.75/1.38 ), ! U = T }.
% 0.75/1.38 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.75/1.38 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.38 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.75/1.38 ), ! Z = Y }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.75/1.38 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.75/1.38 = X }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.75/1.38 tc_Int_Oint ) ) ) }.
% 0.75/1.38 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.75/1.38 tc_Int_Oint ) ) ) }.
% 0.75/1.38 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.75/1.38 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.75/1.38 = Y }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.75/1.38 = Y }.
% 0.75/1.38 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.75/1.38 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.75/1.38 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.75/1.38 ( X, Y ) ) }.
% 0.75/1.38 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.75/1.38 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.75/1.38 ) ), Y ) }.
% 0.75/1.38 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.75/1.38 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.75/1.38 ( X, Y ) ) }.
% 0.75/1.38 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.75/1.38 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.75/1.38 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.75/1.38 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.75/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.75/1.38 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.38 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.38 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.75/1.38 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.75/1.38 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.38 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.75/1.38 ) ), T ), Y ) }.
% 0.75/1.38 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.75/1.38 = Y }.
% 0.75/1.38 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.75/1.38 = Y }.
% 0.75/1.38 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.75/1.38 = Y }.
% 0.75/1.38 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.75/1.38 = Y }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), U ), T ) ), hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.38 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T
% 0.75/1.38 ) ) ) }.
% 0.75/1.38 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.38 ( X ), Y ), T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z
% 0.75/1.38 ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.38 ( X ), Z ), T ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 0.75/1.38 ), Z ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.38 ( X ), T ), Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 0.75/1.38 ), Z ), Y ) ) }.
% 0.75/1.38 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.75/1.38 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.75/1.38 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.75/1.38 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.75/1.38 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.75/1.38 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.75/1.38 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.75/1.38 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.75/1.38 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.75/1.38 .
% 0.75/1.38 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.75/1.38 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.75/1.38 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 0.75/1.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.75/1.38 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 0.75/1.38 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 0.75/1.38 .
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.75/1.38 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.75/1.38 ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.75/1.38 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha10( X, Y
% 0.75/1.38 , Z ), alpha33( X, Y, Z ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha10( X, Y, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha33( X, Y, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.75/1.38 { ! alpha33( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! alpha33( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.75/1.38 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ), alpha33( X, Y, Z ) }.
% 0.75/1.38 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.75/1.38 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Y ), alpha10( X, Y, Z ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( X ) ), alpha11( X, Y, Z ), alpha34( X, Y, Z ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha11( X, Y, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( X ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha34( X, Y, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( X ) ) }.
% 0.75/1.38 { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.75/1.38 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( X ), Y ), alpha34( X, Y, Z ) }.
% 0.75/1.38 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.75/1.38 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ), alpha11( X, Y, Z ) }.
% 0.75/1.38 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.75/1.38 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.38 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.38 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( X ) ) }.
% 0.75/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.38 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.75/1.38 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.75/1.38 { ! class_Rings_Oordered__semiring( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.75/1.38 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.75/1.38 { ! class_Rings_Oordered__semiring( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.75/1.38 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.75/1.38 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.38 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.38 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.75/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.38 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.38 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.75/1.38 { ! class_Rings_Oordered__semiring( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.75/1.38 { ! class_Rings_Oordered__semiring( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.75/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.38 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.75/1.38 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.38 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.75/1.38 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.38 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( X ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.75/1.38 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.75/1.38 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.75/1.38 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.75/1.38 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.75/1.38 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.75/1.38 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.75/1.38 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.75/1.38 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.75/1.38 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( X ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.75/1.38 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.75/1.38 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.75/1.38 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.75/1.38 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.75/1.38 .
% 0.75/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.75/1.38 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.75/1.38 .
% 0.75/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.75/1.38 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.75/1.38 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( X ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.75/1.38 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.75/1.38 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.75/1.38 ( X ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.75/1.38 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.75/1.38 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.75/1.38 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.75/1.38 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.75/1.38 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha12( X, Y, Z, T ),
% 0.75/1.38 alpha35( X, Y, Z, T ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha12( X, Y, Z, T ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha35( X, Y, Z, T ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.75/1.38 { ! alpha35( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! alpha35( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.75/1.38 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha35( X, Y, Z, T ) }.
% 0.75/1.38 { ! alpha12( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.75/1.38 { ! alpha12( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.75/1.38 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha12( X, Y, Z, T ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha13( X, Y, Z, T ),
% 0.75/1.38 alpha36( X, Y, Z, T ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha13( X, Y, Z, T ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha36( X, Y, Z, T ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.75/1.38 { ! alpha36( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! alpha36( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.75/1.38 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha36( X, Y, Z, T ) }.
% 0.75/1.38 { ! alpha13( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.75/1.38 { ! alpha13( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.75/1.38 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha13( X, Y, Z, T ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.75/1.38 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.38 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.75/1.38 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.38 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.75/1.38 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.75/1.38 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.75/1.38 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.38 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 0.75/1.38 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), T =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.75/1.38 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.38 X ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 0.75/1.38 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.38 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 0.75/1.38 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), Z =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.75/1.38 c_Rings_Odvd__class_Odvd( X ), T ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.75/1.38 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.38 X ), T ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 0.75/1.38 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.75/1.38 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.75/1.38 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.75/1.38 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.75/1.38 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.75/1.38 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.75/1.38 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.75/1.38 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.75/1.38 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.75/1.38 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.75/1.38 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.75/1.38 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 0.75/1.38 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 0.75/1.38 X, Z ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.75/1.38 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.75/1.38 ) }.
% 0.75/1.38 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.75/1.38 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.75/1.38 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.75/1.38 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.38 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.75/1.38 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.75/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.75/1.38 c_Groups_Oone__class_Oone( X ) }.
% 0.75/1.38 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.75/1.38 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.75/1.38 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.75/1.38 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.75/1.38 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.75/1.38 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Nat_Onat, Z, Y ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.75/1.38 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.75/1.38 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 0.75/1.38 Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.75/1.38 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.75/1.38 , Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.75/1.38 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.75/1.38 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.75/1.38 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.75/1.38 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.75/1.38 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.75/1.38 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.75/1.38 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.75/1.38 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.75/1.38 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.75/1.38 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.75/1.38 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.75/1.38 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.75/1.38 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.75/1.38 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.75/1.38 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.75/1.38 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.75/1.38 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.75/1.38 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.38 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.75/1.38 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.75/1.38 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.75/1.38 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.75/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.75/1.38 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.75/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.75/1.38 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.75/1.38 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.75/1.38 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.75/1.38 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.75/1.38 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.75/1.38 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.75/1.38 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ),
% 0.75/1.38 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.75/1.38 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 0.75/1.38 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 0.75/1.38 c_Polynomial_Odegree( X, Z ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.75/1.38 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.75/1.38 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.75/1.38 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.75/1.38 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.75/1.38 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.75/1.38 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.75/1.38 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.75/1.38 ) ) }.
% 0.75/1.38 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.75/1.38 ( X, Y ), Z = Y }.
% 0.75/1.38 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.75/1.38 ( X, Y ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.75/1.38 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.75/1.38 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.75/1.38 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.75/1.38 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.38 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.75/1.38 ), Y ) }.
% 0.75/1.38 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.75/1.38 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.75/1.38 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 0.75/1.38 .
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.75/1.38 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 0.75/1.38 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 0.75/1.38 .
% 0.75/1.38 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.75/1.38 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.75/1.38 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.75/1.38 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.75/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.75/1.38 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.75/1.38 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.75/1.38 hAPP( Z, skol13( U, W, Z ) ) ) }.
% 0.75/1.38 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.75/1.38 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.75/1.38 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ),
% 0.75/1.38 c_Groups_Oplus__class_Oplus( X, skol13( X, Y, Z ),
% 0.75/1.38 c_Groups_Ozero__class_Ozero( X ) ) ) ) }.
% 0.75/1.38 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.75/1.38 hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Oplus__class_Oplus( X
% 0.75/1.38 , T, c_Groups_Ozero__class_Ozero( X ) ) ) ), ! hBOOL( hAPP( Z, T ) ),
% 0.75/1.38 hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.75/1.38 skol20( X, Y, Z ) ) ) ) }.
% 0.75/1.38 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.75/1.38 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.75/1.38 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.75/1.38 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.75/1.38 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.75/1.38 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.75/1.38 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.75/1.38 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.75/1.38 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.75/1.38 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.75/1.38 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.75/1.38 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.75/1.38 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.75/1.38 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.75/1.38 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.75/1.38 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.75/1.38 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.75/1.38 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.75/1.38 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.75/1.38 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.75/1.38 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.75/1.38 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.75/1.38 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.75/1.38 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.75/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.75/1.38 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.38 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.75/1.38 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.75/1.38 .
% 0.75/1.38 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.75/1.38 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.75/1.38 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.75/1.38 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.75/1.38 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.39 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.75/1.39 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.75/1.39 .
% 0.75/1.39 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.75/1.39 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.39 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.39 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.39 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.39 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.39 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.75/1.39 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.75/1.39 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.75/1.39 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.75/1.39 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.75/1.39 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.75/1.39 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.75/1.39 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.75/1.39 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.75/1.39 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.75/1.39 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.75/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.75/1.39 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.75/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.75/1.39 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.75/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.75/1.39 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.75/1.39 , Y ), X ) }.
% 0.75/1.39 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.75/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.75/1.39 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.75/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.75/1.39 tc_Nat_Onat ) }.
% 0.75/1.39 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.75/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.75/1.39 tc_Nat_Onat ) }.
% 0.75/1.39 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.75/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.75/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.75/1.39 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.75/1.39 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ) ), hBOOL( hAPP( hAPP(
% 0.75/1.39 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), c_Groups_Oplus__class_Oplus
% 0.75/1.39 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ) ) }.
% 0.75/1.39 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.75/1.39 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.75/1.39 , Z ), X ) ), T ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.39 tc_Int_Oint ), Y ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ) )
% 0.75/1.39 }.
% 0.75/1.39 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ), hBOOL( hAPP
% 0.75/1.39 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.75/1.39 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) )
% 0.75/1.39 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ) }.
% 0.75/1.39 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.75/1.39 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.75/1.39 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.75/1.39 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.75/1.39 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.75/1.39 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.75/1.39 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 0.75/1.39 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.75/1.39 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 0.75/1.39 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 0.75/1.39 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ), hBOOL( hAPP(
% 0.75/1.39 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.75/1.39 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Opcompose( X, Z, Y )
% 0.75/1.39 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.75/1.39 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.75/1.39 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.75/1.39 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.75/1.39 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.75/1.39 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.75/1.39 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.75/1.39 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.75/1.39 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.75/1.39 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.75/1.39 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.75/1.39 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.75/1.39 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Nat_Onat ), Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.75/1.39 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Nat_Onat ), Z ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.75/1.39 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.75/1.39 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.75/1.39 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 Y ), X ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.75/1.39 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.75/1.39 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.75/1.39 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.75/1.39 ), X ) ) }.
% 0.75/1.39 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.75/1.39 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.75/1.39 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.75/1.39 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.75/1.39 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.75/1.39 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.75/1.39 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.75/1.39 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.75/1.39 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.75/1.39 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.75/1.39 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.75/1.39 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.75/1.39 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.75/1.39 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.75/1.39 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.75/1.39 ), X ) ) }.
% 0.75/1.39 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.75/1.39 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.39 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 0.75/1.39 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), Z =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP( hAPP(
% 0.75/1.39 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.75/1.39 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.75/1.39 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.75/1.39 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.75/1.39 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.75/1.39 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.75/1.39 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.75/1.39 ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.75/1.39 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.75/1.39 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Nat_Onat ), Z ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.39 tc_Nat_Onat ), Y ), X ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.75/1.39 ) }.
% 0.75/1.39 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.75/1.39 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.75/1.39 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.75/1.39 ) }.
% 0.75/1.39 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.75/1.39 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.75/1.39 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__1( X ), c_Orderings_Oord__class_Oless__eq
% 0.75/1.39 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 0.75/1.39 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Polynomial_Odegree( X, Z ) ), Y ) ) }.
% 0.75/1.39 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.75/1.39 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.75/1.39 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ) }.
% 0.75/1.39 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.75/1.39 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ), hBOOL( hAPP( hAPP
% 0.75/1.39 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.75/1.39 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.75/1.39 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 0.75/1.39 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) ) }.
% 0.75/1.39 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 0.75/1.39 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) ), hBOOL( hAPP(
% 0.75/1.39 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.39 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 X ), Y ) ), X ) ), Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.75/1.39 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.39 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 Y ), X ) ), X ) ), Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.75/1.39 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ), X ) ) }.
% 0.75/1.39 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Int_Oint ) ) }.
% 0.75/1.39 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.75/1.39 tc_Int_Oint ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Int_Oint, X, Y ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.75/1.39 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.75/1.39 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.75/1.39 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.75/1.39 ( tc_Int_Oint ), Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.75/1.39 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.75/1.39 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.75/1.39 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.75/1.39 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.75/1.39 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.75/1.39 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.75/1.39 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.75/1.39 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.75/1.39 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.75/1.39 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.75/1.39 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.75/1.39 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.75/1.39 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.75/1.39 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.75/1.39 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.75/1.39 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.75/1.39 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.39 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.75/1.39 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.75/1.39 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.39 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 X ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 0.75/1.39 , Y ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.75/1.39 ), Y ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.39 tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.39 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 X ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 0.75/1.39 , Y ) ) ) }.
% 0.75/1.39 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.75/1.39 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.75/1.39 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.75/1.39 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.75/1.39 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.75/1.39 .
% 0.75/1.39 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.75/1.39 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.75/1.39 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.75/1.39 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.75/1.39 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.75/1.39 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.75/1.39 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.39 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.75/1.39 tc_Nat_Onat ), X ), Y ) }.
% 0.75/1.39 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.75/1.39 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), Z =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.75/1.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 0.75/1.39 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.75/1.39 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.75/1.39 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.39 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.75/1.39 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.75/1.39 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 0.75/1.39 }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.75/1.39 , alpha51( X, Y, Z, T ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha51( X, Y, Z, T ),
% 0.75/1.39 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 0.75/1.39 { ! alpha51( X, Y, Z, T ), alpha14( X, Z, T ) }.
% 0.75/1.39 { ! alpha51( X, Y, Z, T ), alpha37( X, Y, T ) }.
% 0.75/1.39 { ! alpha14( X, Z, T ), ! alpha37( X, Y, T ), alpha51( X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha37( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ), alpha52( X, Y, Z ) }.
% 0.75/1.39 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha37( X
% 0.75/1.39 , Y, Z ) }.
% 0.75/1.39 { ! alpha52( X, Y, Z ), alpha37( X, Y, Z ) }.
% 0.75/1.39 { ! alpha52( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.75/1.39 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 0.75/1.39 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha52( X
% 0.75/1.39 , Y, Z ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 0.75/1.39 ), c_Polynomial_Odegree( X, Z ) ), alpha52( X, Y, Z ) }.
% 0.75/1.39 { ! alpha14( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha14( X,
% 0.75/1.39 Y, Z ) }.
% 0.75/1.39 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha14( X
% 0.75/1.39 , Y, Z ) }.
% 0.75/1.39 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.75/1.39 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 0.75/1.39 .
% 0.75/1.39 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.75/1.39 , c_Polynomial_Opdivmod__rel( X, c_Polynomial_Osmult( X, W, U ), T,
% 0.75/1.39 c_Polynomial_Osmult( X, W, Z ), c_Polynomial_Osmult( X, W, Y ) ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.75/1.39 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.75/1.39 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.75/1.39 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.75/1.39 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.75/1.39 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 0.75/1.39 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 0.75/1.39 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 0.75/1.39 ) }.
% 0.75/1.39 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.75/1.39 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.39 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.75/1.39 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.39 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.39 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.39 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.75/1.39 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.75/1.39 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.75/1.39 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.75/1.39 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.75/1.39 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.75/1.39 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.75/1.39 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.75/1.39 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.75/1.39 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.75/1.39 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.75/1.39 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.75/1.39 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.75/1.39 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol14( Z, Y ) ) ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.75/1.39 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 0.75/1.39 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Int_Oint, skol14( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.75/1.39 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.75/1.39 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 0.75/1.39 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 0.75/1.39 ) ) }.
% 0.75/1.39 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.75/1.39 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol15( Z, Y
% 0.75/1.39 ), Y ) }.
% 0.75/1.39 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.75/1.39 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.75/1.39 skol15( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.75/1.39 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.75/1.39 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.75/1.39 , skol15( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.75/1.39 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.75/1.39 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), ! hAPP(
% 0.75/1.39 c_Polynomial_Ocoeff( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 0.75/1.39 , Y ) }.
% 0.75/1.39 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.75/1.39 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.75/1.39 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.75/1.39 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.75/1.39 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.75/1.39 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.75/1.39 c_Polynomial_Odegree( X, Y ) ), ! hBOOL( hAPP( hAPP(
% 0.75/1.39 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), ! hBOOL
% 0.75/1.39 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Y ),
% 0.75/1.39 Z ) ), Z = Y }.
% 0.75/1.39 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.75/1.39 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 0.75/1.39 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.75/1.39 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 }.
% 0.75/1.39 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 0.75/1.39 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.75/1.39 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.75/1.39 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.75/1.39 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.75/1.39 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.75/1.39 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.75/1.39 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.75/1.39 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.75/1.39 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.75/1.39 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.75/1.39 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.75/1.39 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.75/1.39 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.39 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.75/1.39 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.75/1.39 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( X ) ) }.
% 0.75/1.39 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.75/1.39 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.75/1.39 , Z, Y ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.75/1.39 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.75/1.39 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.75/1.39 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.75/1.39 T ) ) ) }.
% 0.75/1.39 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.75/1.39 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.75/1.39 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.75/1.39 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.75/1.39 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.75/1.39 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.75/1.39 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.75/1.39 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) ) }.
% 0.75/1.39 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.75/1.39 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.75/1.39 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 0.75/1.39 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.75/1.39 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.75/1.39 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 0.75/1.39 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.75/1.39 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.75/1.39 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.75/1.39 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.75/1.39 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.75/1.39 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 0.75/1.39 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.75/1.39 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 0.75/1.39 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 0.75/1.39 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 0.75/1.39 c_Polynomial_Ocoeff( X, Y ) }.
% 0.75/1.39 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 0.75/1.39 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 0.75/1.39 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol16( X
% 0.75/1.39 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol16( X, Y, Z ) ), Z =
% 0.75/1.39 Y }.
% 0.75/1.39 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.75/1.39 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.75/1.39 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.75/1.39 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.75/1.39 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.75/1.39 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.75/1.39 hAPP( Z, Y ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.75/1.39 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.75/1.39 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.75/1.39 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.75/1.39 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.75/1.39 ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.75/1.39 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.75/1.39 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.39 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.75/1.39 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.39 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.75/1.39 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.75/1.39 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.75/1.39 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.75/1.39 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.75/1.39 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.75/1.39 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.75/1.39 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.75/1.39 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.75/1.39 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.75/1.39 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.75/1.39 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.39 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.75/1.39 ) }.
% 0.75/1.39 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.75/1.39 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.75/1.39 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.75/1.39 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.75/1.39 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.75/1.39 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.39 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.75/1.39 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 0.75/1.39 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.75/1.39 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 0.75/1.39 ), Y ) ) }.
% 0.75/1.39 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.75/1.39 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Nat_Onat ) ) = Z }.
% 0.75/1.39 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.75/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.75/1.39 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.75/1.39 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Nat_Onat, Z, Y ), X ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Nat_Onat, Z, X ), Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.75/1.39 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.75/1.39 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.75/1.39 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), ! hBOOL( hAPP(
% 0.75/1.39 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), hBOOL( hAPP( hAPP
% 0.75/1.39 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 0.75/1.39 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), ! hBOOL( hAPP(
% 0.75/1.39 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), hBOOL( hAPP( hAPP
% 0.75/1.39 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.75/1.39 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.75/1.39 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.75/1.39 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.75/1.39 ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.75/1.39 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.75/1.39 ) }.
% 0.75/1.39 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Nat_Onat, Z, X ), Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.75/1.39 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.75/1.39 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.75/1.39 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.75/1.39 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.75/1.39 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.39 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.39 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.75/1.39 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.75/1.39 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.75/1.39 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.75/1.39 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.75/1.39 X, Z, Y ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.75/1.39 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.75/1.39 X, Y ) ) }.
% 0.75/1.39 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.75/1.39 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.75/1.39 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.75/1.39 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.75/1.39 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.75/1.39 , Y ) ) }.
% 0.75/1.39 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.75/1.39 X, Y ) }.
% 0.75/1.39 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.39 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.75/1.39 Z ) ), Y ) ) }.
% 0.75/1.39 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.39 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.75/1.39 Z ) ), U ), T ) = Y }.
% 0.75/1.39 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.75/1.39 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.39 ( X ), Z ), U ), Y ) }.
% 0.75/1.39 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.39 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.75/1.39 W ) ), U ), Y ) }.
% 0.75/1.39 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.75/1.39 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.75/1.39 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.39 ( X ), Z ), U ), Y ) }.
% 0.75/1.39 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.75/1.39 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.75/1.39 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.75/1.39 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.75/1.39 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 0.75/1.39 ) ) }.
% 0.75/1.39 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.75/1.39 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.75/1.39 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.75/1.39 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.75/1.39 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.75/1.39 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.75/1.39 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.75/1.39 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.75/1.39 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.75/1.39 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.75/1.39 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.75/1.39 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.75/1.39 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.39 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.39 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.39 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.75/1.39 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.39 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.75/1.39 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.39 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.75/1.39 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.39 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.39 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.39 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.75/1.39 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.39 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.75/1.39 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.39 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.75/1.39 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.39 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.75/1.39 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.75/1.39 X, W, Z ) ), U ), T ), Y ) }.
% 0.75/1.39 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.39 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.75/1.39 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.39 ( X ), Z ), U ), Y ) ) }.
% 0.75/1.39 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.39 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.75/1.39 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.75/1.39 ( X, Z, W ) ), U ), Y ) ) }.
% 0.75/1.39 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.75/1.39 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.75/1.39 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.39 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.75/1.39 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.75/1.39 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.75/1.39 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.75/1.39 .
% 0.75/1.39 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 0.75/1.39 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.75/1.39 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X, U, T
% 0.75/1.39 ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.75/1.39 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 0.75/1.39 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.75/1.39 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, U, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ), hBOOL( hAPP(
% 0.75/1.39 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X
% 0.75/1.39 , U, T ) ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 0.75/1.39 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.75/1.39 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X, U, T
% 0.75/1.39 ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.75/1.39 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 0.75/1.39 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.75/1.39 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, U, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ), hBOOL( hAPP(
% 0.75/1.39 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X
% 0.75/1.39 , U, T ) ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.75/1.39 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.75/1.39 ) ) = X }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.75/1.39 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.75/1.39 , ! alpha15( X, Y, Z ) }.
% 0.75/1.39 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.75/1.39 , ! alpha38( X, Y, Z ) }.
% 0.75/1.39 { alpha15( X, Y, Z ), alpha38( X, Y, Z ), hBOOL( hAPP( Z,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.75/1.39 { ! alpha38( X, Y, Z ), ! hBOOL( hAPP( Z, skol17( T, U, Z ) ) ) }.
% 0.75/1.39 { ! alpha38( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.75/1.39 skol17( X, Y, Z ) ) }.
% 0.75/1.39 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.75/1.39 ) ), alpha38( X, Y, Z ) }.
% 0.75/1.39 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.75/1.39 }.
% 0.75/1.39 { ! alpha15( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Nat_Onat ) ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha15( X, Y, Z ) }.
% 0.75/1.39 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.75/1.39 , alpha16( X, Y, Z ) }.
% 0.75/1.39 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.75/1.39 , alpha39( X, Y, Z ) }.
% 0.75/1.39 { ! alpha16( X, Y, Z ), ! alpha39( X, Y, Z ), hBOOL( hAPP( Z,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.75/1.39 { ! alpha39( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.75/1.39 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.75/1.39 { ! hBOOL( hAPP( Z, skol18( T, U, Z ) ) ), alpha39( X, Y, Z ) }.
% 0.75/1.39 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol18( X, Y, Z ) ),
% 0.75/1.39 alpha39( X, Y, Z ) }.
% 0.75/1.39 { ! alpha16( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.75/1.39 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.75/1.39 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha16( X, Y, Z ) }
% 0.75/1.39 .
% 0.75/1.39 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha16
% 0.75/1.39 ( X, Y, Z ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.75/1.39 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.75/1.39 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 0.75/1.39 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.39 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.75/1.39 tc_Nat_Onat, Y, c_Polynomial_Odegree( X, Z ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.75/1.39 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.75/1.39 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.75/1.39 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.75/1.39 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.39 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.75/1.39 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.75/1.39 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.75/1.39 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 0.75/1.39 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 0.75/1.39 tc_Nat_Onat ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.75/1.39 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.75/1.39 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.75/1.39 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.75/1.39 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.75/1.39 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.75/1.39 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.75/1.39 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.75/1.39 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.75/1.39 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.75/1.39 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.75/1.39 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.75/1.39 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.75/1.39 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.75/1.39 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.75/1.39 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.75/1.39 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.75/1.39 ( tc_Nat_Onat ) ) ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.75/1.39 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.75/1.39 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.75/1.39 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.75/1.39 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.75/1.39 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 0.75/1.39 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.75/1.39 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.75/1.39 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.75/1.39 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.75/1.39 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.75/1.39 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.75/1.39 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 0.75/1.39 ( X ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.75/1.39 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.75/1.39 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.75/1.39 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.75/1.39 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.75/1.39 c_Groups_Oone__class_Oone( X ) }.
% 0.75/1.39 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.75/1.39 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.75/1.39 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.75/1.39 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.75/1.39 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 0.75/1.39 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 0.75/1.39 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.75/1.39 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.75/1.39 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.75/1.39 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) ), ! hBOOL( hAPP(
% 0.75/1.39 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ), hBOOL( hAPP(
% 0.75/1.39 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.75/1.39 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.75/1.39 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.75/1.39 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.75/1.39 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.75/1.39 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.75/1.39 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.75/1.39 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.75/1.39 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.75/1.39 T ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.75/1.39 c_Polynomial_Odegree( X, c_Groups_Ominus__class_Ominus(
% 0.75/1.39 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 0.75/1.39 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.75/1.39 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.75/1.39 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 0.75/1.39 }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.75/1.39 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.75/1.39 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.75/1.39 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.75/1.39 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.75/1.39 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.75/1.39 tc_Polynomial_Opoly( X ), Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.75/1.39 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.75/1.39 .
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.75/1.39 ( tc_Int_Oint ) ) ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.75/1.39 , T = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! V0 =
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 0.75/1.39 c_Polynomial_OpCons( X, W, Y ) ), c_Polynomial_Odegree( X, T ) ), hAPP(
% 0.75/1.39 c_Polynomial_Ocoeff( X, T ), c_Polynomial_Odegree( X, T ) ) ),
% 0.75/1.39 c_Polynomial_Opdivmod__rel( X, c_Polynomial_OpCons( X, W, U ), T,
% 0.75/1.39 c_Polynomial_OpCons( X, V0, Z ), c_Groups_Ominus__class_Ominus(
% 0.75/1.39 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, W, Y ),
% 0.75/1.39 c_Polynomial_Osmult( X, V0, T ) ) ) }.
% 0.75/1.39 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.75/1.39 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.75/1.39 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.75/1.39 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.75/1.39 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.75/1.39 { ! class_RealVector_Oreal__normed__field( X ),
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.75/1.39 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.75/1.39 { ! class_Rings_Odivision__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.75/1.39 ), Y ) }.
% 0.75/1.39 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 0.75/1.39 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.75/1.39 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.75/1.39 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.75/1.39 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.75/1.39 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.39 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.75/1.39 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.75/1.39 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 0.75/1.39 ( X ) }.
% 0.75/1.39 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.75/1.39 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 0.75/1.39 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.75/1.39 c_Groups_Oone__class_Oone( X ) }.
% 0.75/1.39 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 0.75/1.39 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.75/1.39 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.75/1.39 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.39 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 }.
% 0.75/1.39 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 0.75/1.39 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.75/1.39 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.75/1.39 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 0.75/1.39 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.75/1.39 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 , c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X
% 0.75/1.39 , Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.75/1.39 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.75/1.39 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 , c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X
% 0.75/1.39 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.75/1.39 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.75/1.39 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.75/1.39 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.75/1.39 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.75/1.39 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.75/1.39 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.75/1.39 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 0.75/1.39 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.75/1.39 { ! class_RealVector_Oreal__normed__field( X ),
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.75/1.39 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.39 { ! class_RealVector_Oreal__normed__field( X ),
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 0.75/1.39 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 0.75/1.39 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.75/1.39 { ! class_RealVector_Oreal__normed__field( X ),
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.75/1.39 ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ), hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.75/1.39 tc_Nat_Onat, Z, T ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.75/1.39 ( X, Z, Y ) ), alpha40( X, Y, Z, T ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.75/1.39 ( X, Z, Y ) ), alpha53( X, Y, Z, T ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha40( X, Y, Z
% 0.75/1.39 , T ), ! alpha53( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.75/1.39 { ! alpha53( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), Y ), alpha57( X, Y, Z, T ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.75/1.39 , alpha53( X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha57( X, Y, Z, T ), alpha53( X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha57( X, Y, Z, T ), alpha61( X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha57( X, Y, Z, T ), alpha17( X, Y, T ) }.
% 0.75/1.39 { ! alpha61( X, Y, Z, T ), ! alpha17( X, Y, T ), alpha57( X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha61( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.39 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.75/1.39 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.75/1.39 alpha61( X, Y, Z, T ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha61( X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha40( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.75/1.39 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.75/1.39 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.75/1.39 alpha40( X, Y, Z, T ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha40( X, Y, Z, T )
% 0.75/1.39 }.
% 0.75/1.39 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.39 , Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.75/1.39 , alpha17( X, Y, Z ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.75/1.39 ) ), alpha17( X, Y, Z ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.75/1.39 , T, Z ), Y ), alpha41( X, Y, Z, T ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.75/1.39 , T, Z ), Y ), alpha54( X, Y, Z, T ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha41( X, Y, Z
% 0.75/1.39 , T ), ! alpha54( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.75/1.39 { ! alpha54( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), Z ), alpha58( X, Y, Z, T ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.75/1.39 , alpha54( X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha58( X, Y, Z, T ), alpha54( X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha58( X, Y, Z, T ), alpha62( X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha58( X, Y, Z, T ), alpha18( X, Y, Z ) }.
% 0.75/1.39 { ! alpha62( X, Y, Z, T ), ! alpha18( X, Y, Z ), alpha58( X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha62( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.39 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.75/1.39 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.75/1.39 alpha62( X, Y, Z, T ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha62( X, Y, Z, T )
% 0.75/1.39 }.
% 0.75/1.39 { ! alpha41( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 0.75/1.39 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.75/1.39 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.75/1.39 alpha41( X, Y, Z, T ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha41( X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.75/1.39 , c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.75/1.39 , alpha18( X, Y, Z ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 , Y ), alpha18( X, Y, Z ) }.
% 0.75/1.39 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 0.75/1.39 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.75/1.39 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.75/1.39 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.75/1.39 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.75/1.39 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.75/1.39 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.75/1.39 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.75/1.39 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.75/1.39 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.75/1.39 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.75/1.39 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha19( X, Y, Z ), alpha42
% 0.75/1.39 ( X, Y, Z ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha19( X, Y, Z
% 0.75/1.39 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.75/1.39 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha42( X, Y, Z
% 0.75/1.39 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.75/1.39 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.39 { ! alpha42( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.39 { ! alpha42( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.75/1.39 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( X ), Y ), alpha42( X, Y, Z ) }.
% 0.75/1.39 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.75/1.39 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ), alpha19( X, Y, Z ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha20( X, Y, Z ), alpha43
% 0.75/1.39 ( X, Y, Z ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha20( X, Y, Z
% 0.75/1.39 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.75/1.39 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha43( X, Y, Z
% 0.75/1.39 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.75/1.39 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.75/1.39 { ! alpha43( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.39 { ! alpha43( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.75/1.39 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ), alpha43( X, Y, Z ) }.
% 0.75/1.39 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.75/1.39 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), Y ), alpha20( X, Y, Z ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.75/1.39 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.75/1.39 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.75/1.39 , Y, Z ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.75/1.39 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.75/1.39 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.75/1.39 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.75/1.39 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.75/1.39 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.75/1.39 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.75/1.39 , Y, Z ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 0.75/1.39 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha21( X, Y, Z ), alpha44( X,
% 0.75/1.39 Y, Z ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha21( X, Y, Z
% 0.75/1.39 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.75/1.39 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha44( X, Y, Z
% 0.75/1.39 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.75/1.39 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.39 { ! alpha44( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.39 { ! alpha44( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.75/1.39 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.39 ), alpha44( X, Y, Z ) }.
% 0.75/1.39 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.75/1.39 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.75/1.39 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 ), alpha21( X, Y, Z ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha22( X, Y, Z ), alpha45
% 0.75/1.39 ( X, Y, Z ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha22( X, Y, Z
% 0.75/1.39 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha45( X, Y, Z
% 0.75/1.39 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.75/1.39 { ! alpha45( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.39 { ! alpha45( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.75/1.39 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 ), alpha45( X, Y, Z ) }.
% 0.75/1.39 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.75/1.39 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.75/1.39 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.39 ), alpha22( X, Y, Z ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 0.75/1.39 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.75/1.39 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.75/1.39 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.75/1.39 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.75/1.39 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.75/1.39 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha46( X, Y, Z, T ) }.
% 0.75/1.39 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha23( X, Y, Z ) }.
% 0.75/1.39 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha46( X, Y, Z, T ), !
% 0.75/1.39 alpha23( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 0.75/1.39 { ! alpha46( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 0.75/1.39 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.75/1.39 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha46( X, Y, Z, T ) }.
% 0.75/1.39 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha46(
% 0.75/1.39 X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha23( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.39 { Z = c_Groups_Ozero__class_Ozero( X ), alpha23( X, Y, Z ) }.
% 0.75/1.39 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha23( X, Y, Z ) }.
% 0.75/1.39 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha47( X, Y, Z, T ) }.
% 0.75/1.39 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha24( X, Y, T ) }.
% 0.75/1.39 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha47( X, Y, Z, T ), !
% 0.75/1.39 alpha24( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.75/1.39 { ! alpha47( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 0.75/1.39 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.75/1.39 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha47( X, Y, Z, T ) }.
% 0.75/1.39 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha47(
% 0.75/1.39 X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha24( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.39 { Y = c_Groups_Ozero__class_Ozero( X ), alpha24( X, Y, Z ) }.
% 0.75/1.39 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha24( X, Y, Z ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.75/1.39 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.75/1.39 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.75/1.39 X ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.39 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.75/1.39 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.75/1.39 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.39 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.75/1.39 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 0.75/1.39 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.75/1.39 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 0.75/1.39 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.39 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.75/1.39 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.75/1.39 X ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.75/1.39 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.75/1.39 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.75/1.39 Z, Y ) ), alpha48( X, Y, Z, T ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.75/1.39 Z, Y ) ), alpha55( X, Y, Z, T ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha48( X, Y, Z
% 0.75/1.39 , T ), ! alpha55( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.75/1.39 { ! alpha55( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), Y ), alpha59( X, Y, Z, T ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.75/1.39 , alpha55( X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha59( X, Y, Z, T ), alpha55( X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha59( X, Y, Z, T ), alpha63( X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha59( X, Y, Z, T ), alpha25( X, Y, T ) }.
% 0.75/1.39 { ! alpha63( X, Y, Z, T ), ! alpha25( X, Y, T ), alpha59( X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha63( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.75/1.39 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.75/1.39 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.75/1.39 alpha63( X, Y, Z, T ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha63( X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha48( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.75/1.39 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.75/1.39 alpha48( X, Y, Z, T ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha48( X, Y, Z, T )
% 0.75/1.39 }.
% 0.75/1.39 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.75/1.39 , alpha25( X, Y, Z ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.75/1.39 , alpha25( X, Y, Z ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.75/1.39 Z ), Y ), alpha49( X, Y, Z, T ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.75/1.39 Z ), Y ), alpha56( X, Y, Z, T ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha49( X, Y, Z
% 0.75/1.39 , T ), ! alpha56( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.75/1.39 { ! alpha56( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), Z ), alpha60( X, Y, Z, T ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.75/1.39 , alpha56( X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha60( X, Y, Z, T ), alpha56( X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha60( X, Y, Z, T ), alpha64( X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha60( X, Y, Z, T ), alpha26( X, Y, Z ) }.
% 0.75/1.39 { ! alpha64( X, Y, Z, T ), ! alpha26( X, Y, Z ), alpha60( X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha64( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.75/1.39 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.75/1.39 alpha64( X, Y, Z, T ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha64( X, Y, Z, T )
% 0.75/1.39 }.
% 0.75/1.39 { ! alpha49( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.75/1.39 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.75/1.39 alpha49( X, Y, Z, T ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha49( X, Y, Z, T ) }.
% 0.75/1.39 { ! alpha26( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.75/1.39 , alpha26( X, Y, Z ) }.
% 0.75/1.39 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.75/1.39 , alpha26( X, Y, Z ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.75/1.39 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.75/1.39 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.75/1.39 Z, Y ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.75/1.39 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.75/1.39 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.75/1.39 Y ), Z ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.75/1.39 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.75/1.39 Y ), Z ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.75/1.39 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.75/1.39 Z, Y ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.75/1.39 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.75/1.39 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.75/1.39 Z, Y ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.75/1.39 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.75/1.39 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.75/1.39 Y ), Z ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.75/1.39 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.75/1.39 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.75/1.39 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.75/1.39 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.75/1.39 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 0.75/1.39 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.75/1.39 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 0.75/1.39 .
% 0.75/1.39 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.75/1.39 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 0.75/1.39 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.75/1.39 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 0.75/1.39 .
% 0.75/1.39 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.75/1.39 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.75/1.39 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.75/1.39 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.75/1.39 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.75/1.39 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.75/1.39 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.75/1.39 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.75/1.39 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.75/1.39 , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.75/1.39 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.75/1.39 , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.75/1.39 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.75/1.39 , T, Y ), Z ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.75/1.39 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.75/1.39 ( X, Z, Y ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.75/1.39 ( X, Z, Y ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.75/1.39 , T, Y ), Z ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.75/1.39 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.75/1.39 , T, Y ), Z ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.75/1.39 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.75/1.39 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.75/1.39 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.75/1.39 ( X, Z, Y ) ) }.
% 0.75/1.39 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 0.75/1.39 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 0.75/1.39 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.75/1.39 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 0.75/1.39 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.75/1.39 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 0.75/1.39 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T, Z ), Y ) =
% 0.75/1.39 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.75/1.39 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 0.75/1.39 tc_Polynomial_Opoly( X ), Z, Y ) ), c_Polynomial_Osmult( X,
% 0.75/1.39 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 0.75/1.39 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 0.75/1.39 tc_Polynomial_Opoly( X ), Z, Y ) ) ), c_Polynomial_Odegree( X, Y ) ),
% 0.75/1.39 hAPP( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y )
% 0.75/1.39 ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.75/1.39 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.75/1.39 tc_Polynomial_Opoly( X ), Y ) ) = c_Divides_Odiv__class_Omod(
% 0.75/1.39 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.75/1.39 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.75/1.39 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.75/1.39 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.75/1.39 ( X ), Z, Y ) ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.75/1.39 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 0.75/1.39 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Omod(
% 0.75/1.39 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.75/1.39 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T,
% 0.75/1.39 c_Polynomial_Osmult( X, Y, Z ) ) = c_Divides_Odiv__class_Omod(
% 0.75/1.39 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.75/1.39 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.75/1.39 }.
% 0.75/1.39 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.75/1.39 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.75/1.39 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.75/1.39 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.39 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.75/1.39 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 0.75/1.39 , Y, Z ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.39 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.75/1.39 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 0.75/1.39 , Y, Z ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.75/1.39 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 0.75/1.39 Z ) = c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.75/1.39 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.75/1.39 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.75/1.39 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 0.75/1.39 X, Z, Y ) }.
% 0.75/1.39 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.75/1.39 c_Rings_Odvd__class_Odvd( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.75/1.39 ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), T ), Y ) ),
% 0.75/1.39 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), T ), Z ) ) }.
% 0.75/1.39 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.75/1.39 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.75/1.39 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.75/1.39 ( tc_fun( Y, X ) ) }.
% 0.75/1.39 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.75/1.39 ) ) }.
% 0.75/1.39 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.75/1.39 .
% 0.75/1.39 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.75/1.39 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.75/1.39 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.75/1.39 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.75/1.39 tc_Int_Oint ) }.
% 0.75/1.39 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.75/1.39 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.75/1.39 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.75/1.39 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.75/1.39 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.75/1.39 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.75/1.39 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.75/1.39 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.75/1.39 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.75/1.39 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.75/1.39 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.75/1.39 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.75/1.39 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.75/1.39 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.75/1.39 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.75/1.39 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.75/1.39 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.75/1.39 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.75/1.39 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.75/1.39 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.75/1.39 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.75/1.39 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.75/1.39 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.75/1.39 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.75/1.39 { class_Power_Opower( tc_Int_Oint ) }.
% 0.75/1.39 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.75/1.39 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.75/1.39 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.75/1.39 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.75/1.39 tc_Nat_Onat ) }.
% 0.75/1.39 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.75/1.39 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.75/1.39 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.75/1.39 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.75/1.39 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.75/1.39 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.75/1.39 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.75/1.39 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.75/1.39 tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { ! class_Rings_Oidom( X ),
% 0.75/1.39 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.75/1.39 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.75/1.39 ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.75/1.39 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.75/1.39 X ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.75/1.39 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.75/1.39 ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.75/1.39 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.75/1.39 }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.75/1.39 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.75/1.39 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.75/1.39 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.75/1.39 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.75/1.39 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.75/1.39 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.75/1.39 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.75/1.39 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.75/1.39 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ),
% 0.75/1.39 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.75/1.39 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.75/1.39 ( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.75/1.39 ( tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.75/1.39 }.
% 0.75/1.39 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.75/1.39 ) ) }.
% 0.75/1.39 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.75/1.39 .
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.75/1.39 tc_Polynomial_Opoly( X ) ) }.
% 0.75/1.39 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 0.75/1.39 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 0.75/1.39 { alpha66, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.75/1.39 ( tc_Complex_Ocomplex ) ), v_p ), hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.75/1.39 ), v_q ), c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) ) ) ),
% 0.75/1.39 alpha50 }.
% 0.75/1.39 { alpha66, ! alpha27 }.
% 0.75/1.39 { ! alpha66, alpha27 }.
% 0.75/1.39 { ! alpha66, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.39 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), v_p ), hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.75/1.39 ), v_q ), c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) ) ) ) }.
% 0.75/1.39 { ! alpha66, ! alpha50 }.
% 0.75/1.39 { ! alpha27, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.75/1.39 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), v_p ), hAPP( hAPP(
% 0.75/1.39 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.75/1.39 ), v_q ), c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) ) ) ),
% 0.75/1.39 alpha50, alpha66 }.
% 0.75/1.39 { ! alpha50, v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.75/1.39 tc_Complex_Ocomplex ) ) }.
% 0.75/1.39 { ! alpha50, v_q = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.75/1.39 tc_Complex_Ocomplex ) ) }.
% 0.75/1.39 { ! v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.75/1.39 tc_Complex_Ocomplex ) ), ! v_q = c_Groups_Ozero__class_Ozero(
% 0.75/1.39 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), alpha50 }.
% 0.75/1.39 { ! alpha27, ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), X ) =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.75/1.39 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q ), X ) =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.75/1.39 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), skol19 ) =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), alpha27 }.
% 0.75/1.39 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q ), skol19 ) =
% 0.75/1.39 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), alpha27 }.
% 0.75/1.39
% 0.75/1.39 *** allocated 15000 integers for clauses
% 0.75/1.39 *** allocated 22500 integers for clauses
% 0.75/1.39 *** allocated 33750 integers for clauses
% 0.75/1.39 *** allocated 50625 integers for clauses
% 0.75/1.39 *** allocated 75937 integers for clauses
% 0.75/1.39 percentage equality = 0.254194, percentage horn = 0.893154
% 0.75/1.39 This is a problem with some equality
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39
% 0.75/1.39 Options Used:
% 0.75/1.39
% 0.75/1.39 useres = 1
% 0.75/1.39 useparamod = 1
% 0.75/1.39 useeqrefl = 1
% 0.75/1.39 useeqfact = 1
% 0.75/1.39 usefactor = 1
% 0.75/1.39 usesimpsplitting = 0
% 0.75/1.39 usesimpdemod = 5
% 0.75/1.39 usesimpres = 3
% 0.75/1.39
% 0.75/1.39 resimpinuse = 1000
% 0.75/1.39 resimpclauses = 20000
% 0.75/1.39 substype = eqrewr
% 0.75/1.39 backwardsubs = 1
% 0.75/1.39 selectoldest = 5
% 0.75/1.39
% 0.75/1.39 litorderings [0] = split
% 0.75/1.39 litorderings [1] = extend the termordering, first sorting on arguments
% 0.75/1.39
% 0.75/1.39 termordering = kbo
% 0.75/1.39
% 0.75/1.39 litapriori = 0
% 0.75/1.39 termapriori = 1
% 0.75/1.39 litaposteriori = 0
% 0.75/1.39 termaposteriori = 0
% 0.75/1.39 demodaposteriori = 0
% 0.75/1.39 ordereqreflfact = 0
% 0.75/1.39
% 0.75/1.39 litselect = negord
% 0.75/1.39
% 0.75/1.39 maxweight = 15
% 0.75/1.39 maxdepth = 30000
% 0.75/1.39 maxlength = 115
% 0.75/1.39 maxnrvars = 195
% 0.75/1.39 excuselevel = 1
% 0.75/1.39 increasemaxweight = 1
% 0.75/1.39
% 0.75/1.39 maxselected = 10000000
% 0.75/1.39 maxnrclauses = 10000000
% 0.75/1.39
% 0.75/1.39 showgenerated = 0
% 0.75/1.39 showkept = 0
% 0.75/1.39 showselected = 0
% 0.75/1.39 showdeleted = 0
% 0.75/1.39 showresimp = 1
% 0.75/1.39 showstatus = 2000
% 0.75/1.39
% 0.75/1.39 prologoutput = 0
% 0.75/1.39 nrgoals = 5000000
% 0.75/1.39 totalproof = 1
% 0.75/1.39
% 0.75/1.39 Symbols occurring in the translation:
% 0.75/1.39
% 0.75/1.39 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.75/1.39 . [1, 2] (w:1, o:196, a:1, s:1, b:0),
% 0.75/1.39 ! [4, 1] (w:0, o:113, a:1, s:1, b:0),
% 0.75/1.39 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.75/1.39 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.75/1.39 hAPP [38, 2] (w:1, o:220, a:1, s:1, b:0),
% 0.75/1.39 v_p [39, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.75/1.39 tc_Complex_Ocomplex [40, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.75/1.39 tc_Polynomial_Opoly [41, 1] (w:1, o:119, a:1, s:1, b:0),
% 0.75/1.39 c_Groups_Ozero__class_Ozero [42, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.75/1.39 c_Polynomial_Odegree [43, 2] (w:1, o:222, a:1, s:1, b:0),
% 0.75/1.39 tc_Nat_Onat [44, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.75/1.39 v_n____ [45, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.75/1.39 c_Nat_OSuc [46, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.75/1.39 c_Polynomial_Opoly [47, 2] (w:1, o:223, a:1, s:1, b:0),
% 0.75/1.39 v_q [48, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.75/1.39 c_Rings_Odvd__class_Odvd [49, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.75/1.39 c_Power_Opower__class_Opower [50, 1] (w:1, o:123, a:1, s:1, b:0),
% 0.75/1.39 hBOOL [51, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.75/1.39 class_Rings_Ocomm__semiring__1 [55, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.75/1.39 class_Rings_Ocomm__semiring__0 [59, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.75/1.39 class_Int_Oring__char__0 [61, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.75/1.39 class_Rings_Oidom [62, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.75/1.39 class_Power_Opower [66, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.75/1.39 class_Rings_Omult__zero [67, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.75/1.39 class_Rings_Ono__zero__divisors [68, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.75/1.39
% 0.75/1.39 class_Rings_Ozero__neq__one [69, 1] (w:1, o:147, a:1, s:1, b:0),
% 0.75/1.39 class_Rings_Oring__1__no__zero__divisors [70, 1] (w:1, o:148, a:1, s:
% 0.75/1.39 1, b:0),
% 0.75/1.39 c_Polynomial_Oorder [72, 3] (w:1, o:246, a:1, s:1, b:0),
% 0.75/1.39 class_Rings_Osemiring__0 [75, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.75/1.39 class_Groups_Ozero [76, 1] (w:1, o:157, a:1, s:1, b:0),
% 0.75/1.39 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [82, 2] (w:1, o:224
% 0.75/1.39 , a:1, s:1, b:0),
% 0.75/1.39 c_Polynomial_Osynthetic__div [87, 3] (w:1, o:247, a:1, s:1, b:0),
% 0.75/1.39 c_Polynomial_Opoly__rec [95, 5] (w:1, o:319, a:1, s:1, b:0),
% 0.75/1.39 c_Polynomial_OpCons [96, 3] (w:1, o:248, a:1, s:1, b:0),
% 0.75/1.39 c_Orderings_Oord__class_Oless__eq [97, 3] (w:1, o:244, a:1, s:1, b:0)
% 0.75/1.39 ,
% 0.75/1.39 tc_Int_Oint [99, 0] (w:1, o:73, a:1, s:1, b:0),
% 0.75/1.39 class_Fields_Ofield [100, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.75/1.39 c_Polynomial_Osmult [101, 3] (w:1, o:249, a:1, s:1, b:0),
% 0.75/1.39 c_fequal [103, 2] (w:1, o:225, a:1, s:1, b:0),
% 0.75/1.39 c_If [104, 4] (w:1, o:293, a:1, s:1, b:0),
% 0.75/1.39 class_Rings_Olinordered__semidom [105, 1] (w:1, o:138, a:1, s:1, b:0)
% 0.75/1.39 ,
% 0.75/1.39 class_Orderings_Opreorder [106, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.75/1.39 class_Orderings_Oorder [107, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.75/1.39 c_Orderings_Oorder_Omono [108, 4] (w:1, o:294, a:1, s:1, b:0),
% 0.75/1.39 c_Groups_Oplus__class_Oplus [110, 3] (w:1, o:251, a:1, s:1, b:0),
% 0.75/1.39 c_Groups_Oone__class_Oone [111, 1] (w:1, o:158, a:1, s:1, b:0),
% 0.75/1.39 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [113, 3] (w:
% 0.75/1.39 1, o:250, a:1, s:1, b:0),
% 0.75/1.39 c_Polynomial_Omonom [114, 3] (w:1, o:252, a:1, s:1, b:0),
% 0.75/1.39 c_Orderings_Oord__class_Oless [115, 3] (w:1, o:245, a:1, s:1, b:0),
% 0.75/1.39 class_Groups_Ocomm__monoid__add [117, 1] (w:1, o:159, a:1, s:1, b:0)
% 0.75/1.39 ,
% 0.75/1.39 class_Rings_Olinordered__idom [118, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.75/1.39 class_Orderings_Olinorder [119, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.75/1.39 class_Orderings_Oord [120, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.75/1.39 class_Groups_Omonoid__mult [124, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.75/1.39 tc_fun [128, 2] (w:1, o:234, a:1, s:1, b:0),
% 0.75/1.39 class_Groups_Oordered__comm__monoid__add [129, 1] (w:1, o:162, a:1
% 0.75/1.39 , s:1, b:0),
% 0.75/1.39 class_Groups_Oab__semigroup__add [133, 1] (w:1, o:163, a:1, s:1, b:0)
% 0.75/1.39 ,
% 0.75/1.39 class_Groups_Ocancel__semigroup__add [134, 1] (w:1, o:164, a:1, s:1
% 0.75/1.40 , b:0),
% 0.75/1.40 class_Groups_Ocancel__ab__semigroup__add [135, 1] (w:1, o:165, a:1
% 0.75/1.40 , s:1, b:0),
% 0.75/1.40 class_Groups_Oone [136, 1] (w:1, o:166, a:1, s:1, b:0),
% 0.75/1.40 class_Groups_Omonoid__add [137, 1] (w:1, o:167, a:1, s:1, b:0),
% 0.75/1.40 class_Groups_Olinordered__ab__group__add [138, 1] (w:1, o:160, a:1
% 0.75/1.40 , s:1, b:0),
% 0.75/1.40 class_Groups_Oordered__ab__semigroup__add__imp__le [139, 1] (w:1, o:
% 0.75/1.40 168, a:1, s:1, b:0),
% 0.75/1.40 class_Groups_Oordered__ab__semigroup__add [140, 1] (w:1, o:169, a:1
% 0.75/1.40 , s:1, b:0),
% 0.75/1.40 class_Groups_Oordered__cancel__ab__semigroup__add [142, 1] (w:1, o:
% 0.75/1.40 170, a:1, s:1, b:0),
% 0.75/1.40 c_Groups_Ouminus__class_Ouminus [143, 2] (w:1, o:235, a:1, s:1, b:0)
% 0.75/1.40 ,
% 0.75/1.40 class_Groups_Ogroup__add [144, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.75/1.40 class_Rings_Ocomm__ring [145, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.75/1.40 class_Groups_Oab__group__add [146, 1] (w:1, o:172, a:1, s:1, b:0),
% 0.75/1.40 class_Groups_Oordered__ab__group__add [147, 1] (w:1, o:173, a:1, s:1
% 0.75/1.40 , b:0),
% 0.75/1.40 class_Rings_Ocomm__ring__1 [148, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.75/1.40 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.75/1.40 149, 1] (w:1, o:186, a:1, s:1, b:0),
% 0.75/1.40 c_Groups_Otimes__class_Otimes [150, 1] (w:1, o:187, a:1, s:1, b:0),
% 0.75/1.40 c_Polynomial_Opos__poly [152, 2] (w:1, o:236, a:1, s:1, b:0),
% 0.75/1.40 class_Lattices_Oboolean__algebra [153, 1] (w:1, o:189, a:1, s:1, b:0)
% 0.75/1.40 ,
% 0.75/1.40 class_Rings_Oring [159, 1] (w:1, o:149, a:1, s:1, b:0),
% 0.75/1.40 class_Rings_Oring__no__zero__divisors [164, 1] (w:1, o:150, a:1, s:1
% 0.75/1.40 , b:0),
% 0.75/1.40 class_Rings_Ocomm__semiring [165, 1] (w:1, o:174, a:1, s:1, b:0),
% 0.75/1.40 class_Rings_Osemiring [167, 1] (w:1, o:175, a:1, s:1, b:0),
% 0.75/1.40 class_Groups_Ocomm__monoid__mult [168, 1] (w:1, o:190, a:1, s:1, b:0)
% 0.75/1.40 ,
% 0.75/1.40 class_Rings_Odvd [169, 1] (w:1, o:176, a:1, s:1, b:0),
% 0.75/1.40 class_Lattices_Oab__semigroup__idem__mult [170, 1] (w:1, o:188, a:1
% 0.75/1.40 , s:1, b:0),
% 0.75/1.40 class_Groups_Oab__semigroup__mult [171, 1] (w:1, o:191, a:1, s:1, b:0
% 0.75/1.40 ),
% 0.75/1.40 class_Rings_Olinordered__ring [172, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.75/1.40 class_Rings_Olinordered__ring__strict [173, 1] (w:1, o:137, a:1, s:1
% 0.75/1.40 , b:0),
% 0.75/1.40 class_Rings_Oordered__cancel__semiring [174, 1] (w:1, o:177, a:1, s:1
% 0.75/1.40 , b:0),
% 0.75/1.40 class_Rings_Oordered__ring [175, 1] (w:1, o:178, a:1, s:1, b:0),
% 0.75/1.40 class_Rings_Oordered__semiring [176, 1] (w:1, o:179, a:1, s:1, b:0),
% 0.75/1.40
% 0.75/1.40 class_Rings_Oordered__comm__semiring [177, 1] (w:1, o:180, a:1, s:1
% 0.75/1.40 , b:0),
% 0.75/1.40 class_Rings_Olinordered__comm__semiring__strict [178, 1] (w:1, o:140
% 0.75/1.40 , a:1, s:1, b:0),
% 0.75/1.40 class_Rings_Olinordered__semiring__strict [179, 1] (w:1, o:141, a:1
% 0.75/1.40 , s:1, b:0),
% 0.75/1.40 class_Rings_Olinordered__semiring [180, 1] (w:1, o:142, a:1, s:1, b:0
% 0.75/1.40 ),
% 0.75/1.40 class_Rings_Oring__1 [181, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.75/1.40 class_Groups_Ouminus [183, 1] (w:1, o:192, a:1, s:1, b:0),
% 0.75/1.40 class_Rings_Olinordered__semiring__1 [186, 1] (w:1, o:143, a:1, s:1
% 0.75/1.40 , b:0),
% 0.75/1.40 class_Rings_Olinordered__semiring__1__strict [187, 1] (w:1, o:144, a:
% 0.75/1.40 1, s:1, b:0),
% 0.75/1.40 c_Polynomial_Opcompose [188, 3] (w:1, o:253, a:1, s:1, b:0),
% 0.75/1.40 c_Power_Opower_Opower [189, 3] (w:1, o:254, a:1, s:1, b:0),
% 0.75/1.40 c_Polynomial_Opdivmod__rel [200, 5] (w:1, o:320, a:1, s:1, b:0),
% 0.75/1.40 class_RealVector_Oreal__normed__algebra [201, 1] (w:1, o:181, a:1, s:
% 0.75/1.40 1, b:0),
% 0.75/1.40 c_Polynomial_Ocoeff [210, 2] (w:1, o:221, a:1, s:1, b:0),
% 0.75/1.40 c_Groups_Ominus__class_Ominus [211, 3] (w:1, o:255, a:1, s:1, b:0),
% 0.75/1.40 class_Groups_Ominus [213, 1] (w:1, o:193, a:1, s:1, b:0),
% 0.75/1.40 c_Rings_Oinverse__class_Odivide [220, 3] (w:1, o:256, a:1, s:1, b:0)
% 0.75/1.40 ,
% 0.75/1.40 class_Rings_Odivision__ring [221, 1] (w:1, o:182, a:1, s:1, b:0),
% 0.75/1.40 class_RealVector_Oreal__normed__field [222, 1] (w:1, o:183, a:1, s:1
% 0.75/1.40 , b:0),
% 0.75/1.40 class_Rings_Odivision__ring__inverse__zero [223, 1] (w:1, o:184, a:1
% 0.75/1.40 , s:1, b:0),
% 0.75/1.40 class_Fields_Ofield__inverse__zero [224, 1] (w:1, o:154, a:1, s:1, b:
% 0.75/1.40 0),
% 0.75/1.40 class_Fields_Olinordered__field__inverse__zero [225, 1] (w:1, o:155
% 0.75/1.40 , a:1, s:1, b:0),
% 0.75/1.40 class_Fields_Olinordered__field [226, 1] (w:1, o:156, a:1, s:1, b:0)
% 4.01/4.43 ,
% 4.01/4.43 class_RealVector_Oreal__field [227, 1] (w:1, o:185, a:1, s:1, b:0),
% 4.01/4.43 c_Divides_Odiv__class_Omod [228, 3] (w:1, o:257, a:1, s:1, b:0),
% 4.01/4.43 class_Divides_Osemiring__div [229, 1] (w:1, o:194, a:1, s:1, b:0),
% 4.01/4.43 class_Groups_Ocancel__comm__monoid__add [231, 1] (w:1, o:195, a:1, s:
% 4.01/4.43 1, b:0),
% 4.01/4.43 tc_HOL_Obool [233, 0] (w:1, o:72, a:1, s:1, b:0),
% 4.01/4.43 alpha1 [234, 0] (w:1, o:106, a:1, s:1, b:1),
% 4.01/4.43 alpha2 [235, 0] (w:1, o:107, a:1, s:1, b:1),
% 4.01/4.43 alpha3 [236, 2] (w:1, o:237, a:1, s:1, b:1),
% 4.01/4.43 alpha4 [237, 2] (w:1, o:240, a:1, s:1, b:1),
% 4.01/4.43 alpha5 [238, 3] (w:1, o:262, a:1, s:1, b:1),
% 4.01/4.43 alpha6 [239, 2] (w:1, o:241, a:1, s:1, b:1),
% 4.01/4.43 alpha7 [240, 2] (w:1, o:242, a:1, s:1, b:1),
% 4.01/4.43 alpha8 [241, 2] (w:1, o:243, a:1, s:1, b:1),
% 4.01/4.43 alpha9 [242, 3] (w:1, o:263, a:1, s:1, b:1),
% 4.01/4.43 alpha10 [243, 3] (w:1, o:264, a:1, s:1, b:1),
% 4.01/4.43 alpha11 [244, 3] (w:1, o:265, a:1, s:1, b:1),
% 4.01/4.43 alpha12 [245, 4] (w:1, o:295, a:1, s:1, b:1),
% 4.01/4.43 alpha13 [246, 4] (w:1, o:296, a:1, s:1, b:1),
% 4.01/4.43 alpha14 [247, 3] (w:1, o:266, a:1, s:1, b:1),
% 4.01/4.43 alpha15 [248, 3] (w:1, o:267, a:1, s:1, b:1),
% 4.01/4.43 alpha16 [249, 3] (w:1, o:268, a:1, s:1, b:1),
% 4.01/4.43 alpha17 [250, 3] (w:1, o:269, a:1, s:1, b:1),
% 4.01/4.43 alpha18 [251, 3] (w:1, o:270, a:1, s:1, b:1),
% 4.01/4.43 alpha19 [252, 3] (w:1, o:271, a:1, s:1, b:1),
% 4.01/4.43 alpha20 [253, 3] (w:1, o:272, a:1, s:1, b:1),
% 4.01/4.43 alpha21 [254, 3] (w:1, o:273, a:1, s:1, b:1),
% 4.01/4.43 alpha22 [255, 3] (w:1, o:274, a:1, s:1, b:1),
% 4.01/4.43 alpha23 [256, 3] (w:1, o:275, a:1, s:1, b:1),
% 4.01/4.43 alpha24 [257, 3] (w:1, o:276, a:1, s:1, b:1),
% 4.01/4.43 alpha25 [258, 3] (w:1, o:277, a:1, s:1, b:1),
% 4.01/4.43 alpha26 [259, 3] (w:1, o:278, a:1, s:1, b:1),
% 4.01/4.43 alpha27 [260, 0] (w:1, o:108, a:1, s:1, b:1),
% 4.01/4.43 alpha28 [261, 0] (w:1, o:109, a:1, s:1, b:1),
% 4.01/4.43 alpha29 [262, 0] (w:1, o:110, a:1, s:1, b:1),
% 4.01/4.43 alpha30 [263, 4] (w:1, o:297, a:1, s:1, b:1),
% 4.01/4.43 alpha31 [264, 2] (w:1, o:238, a:1, s:1, b:1),
% 4.01/4.43 alpha32 [265, 2] (w:1, o:239, a:1, s:1, b:1),
% 4.01/4.43 alpha33 [266, 3] (w:1, o:279, a:1, s:1, b:1),
% 4.01/4.43 alpha34 [267, 3] (w:1, o:280, a:1, s:1, b:1),
% 4.01/4.43 alpha35 [268, 4] (w:1, o:298, a:1, s:1, b:1),
% 4.01/4.43 alpha36 [269, 4] (w:1, o:299, a:1, s:1, b:1),
% 4.01/4.43 alpha37 [270, 3] (w:1, o:281, a:1, s:1, b:1),
% 4.01/4.43 alpha38 [271, 3] (w:1, o:282, a:1, s:1, b:1),
% 4.01/4.43 alpha39 [272, 3] (w:1, o:283, a:1, s:1, b:1),
% 4.01/4.43 alpha40 [273, 4] (w:1, o:300, a:1, s:1, b:1),
% 4.01/4.43 alpha41 [274, 4] (w:1, o:301, a:1, s:1, b:1),
% 4.01/4.43 alpha42 [275, 3] (w:1, o:258, a:1, s:1, b:1),
% 4.01/4.43 alpha43 [276, 3] (w:1, o:259, a:1, s:1, b:1),
% 4.01/4.43 alpha44 [277, 3] (w:1, o:260, a:1, s:1, b:1),
% 4.01/4.43 alpha45 [278, 3] (w:1, o:261, a:1, s:1, b:1),
% 4.01/4.43 alpha46 [279, 4] (w:1, o:302, a:1, s:1, b:1),
% 4.01/4.43 alpha47 [280, 4] (w:1, o:303, a:1, s:1, b:1),
% 4.01/4.43 alpha48 [281, 4] (w:1, o:304, a:1, s:1, b:1),
% 4.01/4.43 alpha49 [282, 4] (w:1, o:305, a:1, s:1, b:1),
% 4.01/4.43 alpha50 [283, 0] (w:1, o:111, a:1, s:1, b:1),
% 4.01/4.43 alpha51 [284, 4] (w:1, o:306, a:1, s:1, b:1),
% 4.01/4.43 alpha52 [285, 3] (w:1, o:284, a:1, s:1, b:1),
% 4.01/4.43 alpha53 [286, 4] (w:1, o:307, a:1, s:1, b:1),
% 4.01/4.43 alpha54 [287, 4] (w:1, o:308, a:1, s:1, b:1),
% 4.01/4.43 alpha55 [288, 4] (w:1, o:309, a:1, s:1, b:1),
% 4.01/4.43 alpha56 [289, 4] (w:1, o:310, a:1, s:1, b:1),
% 4.01/4.43 alpha57 [290, 4] (w:1, o:311, a:1, s:1, b:1),
% 4.01/4.43 alpha58 [291, 4] (w:1, o:312, a:1, s:1, b:1),
% 4.01/4.43 alpha59 [292, 4] (w:1, o:313, a:1, s:1, b:1),
% 4.01/4.43 alpha60 [293, 4] (w:1, o:314, a:1, s:1, b:1),
% 4.01/4.43 alpha61 [294, 4] (w:1, o:315, a:1, s:1, b:1),
% 4.01/4.43 alpha62 [295, 4] (w:1, o:316, a:1, s:1, b:1),
% 4.01/4.43 alpha63 [296, 4] (w:1, o:317, a:1, s:1, b:1),
% 4.01/4.43 alpha64 [297, 4] (w:1, o:318, a:1, s:1, b:1),
% 4.01/4.43 alpha65 [298, 3] (w:1, o:285, a:1, s:1, b:1),
% 4.01/4.43 alpha66 [299, 0] (w:1, o:112, a:1, s:1, b:1),
% 4.01/4.43 alpha67 [300, 3] (w:1, o:286, a:1, s:1, b:1),
% 4.01/4.43 skol1 [301, 2] (w:1, o:226, a:1, s:1, b:1),
% 4.01/4.43 skol2 [302, 0] (w:1, o:13, a:1, s:1, b:1),
% 4.01/4.43 skol3 [303, 0] (w:1, o:14, a:1, s:1, b:1),
% 33.14/33.55 skol4 [304, 0] (w:1, o:15, a:1, s:1, b:1),
% 33.14/33.55 skol5 [305, 2] (w:1, o:227, a:1, s:1, b:1),
% 33.14/33.55 skol6 [306, 0] (w:1, o:16, a:1, s:1, b:1),
% 33.14/33.55 skol7 [307, 2] (w:1, o:228, a:1, s:1, b:1),
% 33.14/33.55 skol8 [308, 1] (w:1, o:118, a:1, s:1, b:1),
% 33.14/33.55 skol9 [309, 3] (w:1, o:287, a:1, s:1, b:1),
% 33.14/33.55 skol10 [310, 2] (w:1, o:229, a:1, s:1, b:1),
% 33.14/33.55 skol11 [311, 2] (w:1, o:230, a:1, s:1, b:1),
% 33.14/33.55 skol12 [312, 2] (w:1, o:231, a:1, s:1, b:1),
% 33.14/33.55 skol13 [313, 3] (w:1, o:288, a:1, s:1, b:1),
% 33.14/33.55 skol14 [314, 2] (w:1, o:232, a:1, s:1, b:1),
% 33.14/33.55 skol15 [315, 2] (w:1, o:233, a:1, s:1, b:1),
% 33.14/33.55 skol16 [316, 3] (w:1, o:289, a:1, s:1, b:1),
% 33.14/33.55 skol17 [317, 3] (w:1, o:290, a:1, s:1, b:1),
% 33.14/33.55 skol18 [318, 3] (w:1, o:291, a:1, s:1, b:1),
% 33.14/33.55 skol19 [319, 0] (w:1, o:12, a:1, s:1, b:1),
% 33.14/33.55 skol20 [320, 3] (w:1, o:292, a:1, s:1, b:1).
% 33.14/33.55
% 33.14/33.55
% 33.14/33.55 Starting Search:
% 33.14/33.55
% 33.14/33.55 *** allocated 113905 integers for clauses
% 33.14/33.55 *** allocated 170857 integers for clauses
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55
% 33.14/33.55 Intermediate Status:
% 33.14/33.55 Generated: 2923
% 33.14/33.55 Kept: 2000
% 33.14/33.55 Inuse: 66
% 33.14/33.55 Deleted: 9
% 33.14/33.55 Deletedinuse: 0
% 33.14/33.55
% 33.14/33.55 *** allocated 256285 integers for clauses
% 33.14/33.55 *** allocated 170857 integers for termspace/termends
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55 *** allocated 256285 integers for termspace/termends
% 33.14/33.55
% 33.14/33.55 Intermediate Status:
% 33.14/33.55 Generated: 7483
% 33.14/33.55 Kept: 4127
% 33.14/33.55 Inuse: 156
% 33.14/33.55 Deleted: 15
% 33.14/33.55 Deletedinuse: 0
% 33.14/33.55
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55 *** allocated 384427 integers for clauses
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55
% 33.14/33.55 Intermediate Status:
% 33.14/33.55 Generated: 14018
% 33.14/33.55 Kept: 6460
% 33.14/33.55 Inuse: 259
% 33.14/33.55 Deleted: 22
% 33.14/33.55 Deletedinuse: 0
% 33.14/33.55
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55 *** allocated 576640 integers for clauses
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55 *** allocated 384427 integers for termspace/termends
% 33.14/33.55
% 33.14/33.55 Intermediate Status:
% 33.14/33.55 Generated: 18400
% 33.14/33.55 Kept: 8992
% 33.14/33.55 Inuse: 294
% 33.14/33.55 Deleted: 22
% 33.14/33.55 Deletedinuse: 0
% 33.14/33.55
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55
% 33.14/33.55 Intermediate Status:
% 33.14/33.55 Generated: 24693
% 33.14/33.55 Kept: 11480
% 33.14/33.55 Inuse: 339
% 33.14/33.55 Deleted: 22
% 33.14/33.55 Deletedinuse: 0
% 33.14/33.55
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55 *** allocated 864960 integers for clauses
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55 *** allocated 576640 integers for termspace/termends
% 33.14/33.55
% 33.14/33.55 Intermediate Status:
% 33.14/33.55 Generated: 30877
% 33.14/33.55 Kept: 13708
% 33.14/33.55 Inuse: 373
% 33.14/33.55 Deleted: 27
% 33.14/33.55 Deletedinuse: 4
% 33.14/33.55
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55
% 33.14/33.55 Intermediate Status:
% 33.14/33.55 Generated: 35893
% 33.14/33.55 Kept: 15715
% 33.14/33.55 Inuse: 398
% 33.14/33.55 Deleted: 29
% 33.14/33.55 Deletedinuse: 4
% 33.14/33.55
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55 *** allocated 1297440 integers for clauses
% 33.14/33.55
% 33.14/33.55 Intermediate Status:
% 33.14/33.55 Generated: 41821
% 33.14/33.55 Kept: 18841
% 33.14/33.55 Inuse: 426
% 33.14/33.55 Deleted: 29
% 33.14/33.55 Deletedinuse: 4
% 33.14/33.55
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55 Resimplifying clauses:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55 *** allocated 864960 integers for termspace/termends
% 33.14/33.55
% 33.14/33.55 Intermediate Status:
% 33.14/33.55 Generated: 47017
% 33.14/33.55 Kept: 21056
% 33.14/33.55 Inuse: 441
% 33.14/33.55 Deleted: 267
% 33.14/33.55 Deletedinuse: 4
% 33.14/33.55
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55
% 33.14/33.55 Intermediate Status:
% 33.14/33.55 Generated: 55557
% 33.14/33.55 Kept: 23745
% 33.14/33.55 Inuse: 466
% 33.14/33.55 Deleted: 272
% 33.14/33.55 Deletedinuse: 9
% 33.14/33.55
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55
% 33.14/33.55 Intermediate Status:
% 33.14/33.55 Generated: 60221
% 33.14/33.55 Kept: 25754
% 33.14/33.55 Inuse: 491
% 33.14/33.55 Deleted: 272
% 33.14/33.55 Deletedinuse: 9
% 33.14/33.55
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55 *** allocated 1946160 integers for clauses
% 33.14/33.55
% 33.14/33.55 Intermediate Status:
% 33.14/33.55 Generated: 65019
% 33.14/33.55 Kept: 28484
% 33.14/33.55 Inuse: 511
% 33.14/33.55 Deleted: 272
% 33.14/33.55 Deletedinuse: 9
% 33.14/33.55
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55
% 33.14/33.55 Intermediate Status:
% 33.14/33.55 Generated: 69835
% 33.14/33.55 Kept: 30676
% 33.14/33.55 Inuse: 546
% 33.14/33.55 Deleted: 272
% 33.14/33.55 Deletedinuse: 9
% 33.14/33.55
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55
% 33.14/33.55 Intermediate Status:
% 33.14/33.55 Generated: 73511
% 33.14/33.55 Kept: 32699
% 33.14/33.55 Inuse: 560
% 33.14/33.55 Deleted: 272
% 33.14/33.55 Deletedinuse: 9
% 33.14/33.55
% 33.14/33.55 *** allocated 1297440 integers for termspace/termends
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55
% 33.14/33.55 Intermediate Status:
% 33.14/33.55 Generated: 79369
% 33.14/33.55 Kept: 34713
% 33.14/33.55 Inuse: 577
% 33.14/33.55 Deleted: 272
% 33.14/33.55 Deletedinuse: 9
% 33.14/33.55
% 33.14/33.55 Resimplifying inuse:
% 33.14/33.55 Done
% 33.14/33.55
% 33.14/33.55
% 33.14/33.55 Intermediate Status:
% 100.90/101.36 Generated: 90384
% 100.90/101.36 Kept: 36780
% 100.90/101.36 Inuse: 591
% 100.90/101.36 Deleted: 272
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 99169
% 100.90/101.36 Kept: 39633
% 100.90/101.36 Inuse: 616
% 100.90/101.36 Deleted: 272
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36 Resimplifying clauses:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 106371
% 100.90/101.36 Kept: 41973
% 100.90/101.36 Inuse: 626
% 100.90/101.36 Deleted: 336
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36 *** allocated 2919240 integers for clauses
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 116757
% 100.90/101.36 Kept: 44003
% 100.90/101.36 Inuse: 644
% 100.90/101.36 Deleted: 336
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36 *** allocated 1946160 integers for termspace/termends
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 125313
% 100.90/101.36 Kept: 46564
% 100.90/101.36 Inuse: 661
% 100.90/101.36 Deleted: 336
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 132878
% 100.90/101.36 Kept: 48575
% 100.90/101.36 Inuse: 685
% 100.90/101.36 Deleted: 336
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 145001
% 100.90/101.36 Kept: 50668
% 100.90/101.36 Inuse: 701
% 100.90/101.36 Deleted: 336
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 152358
% 100.90/101.36 Kept: 52737
% 100.90/101.36 Inuse: 716
% 100.90/101.36 Deleted: 336
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 162361
% 100.90/101.36 Kept: 54823
% 100.90/101.36 Inuse: 746
% 100.90/101.36 Deleted: 336
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 170767
% 100.90/101.36 Kept: 56828
% 100.90/101.36 Inuse: 767
% 100.90/101.36 Deleted: 336
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 183262
% 100.90/101.36 Kept: 59798
% 100.90/101.36 Inuse: 776
% 100.90/101.36 Deleted: 336
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36 Resimplifying clauses:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 196831
% 100.90/101.36 Kept: 63022
% 100.90/101.36 Inuse: 841
% 100.90/101.36 Deleted: 478
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36 *** allocated 4378860 integers for clauses
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 203828
% 100.90/101.36 Kept: 67132
% 100.90/101.36 Inuse: 856
% 100.90/101.36 Deleted: 478
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 211388
% 100.90/101.36 Kept: 69450
% 100.90/101.36 Inuse: 901
% 100.90/101.36 Deleted: 478
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36 *** allocated 2919240 integers for termspace/termends
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 222962
% 100.90/101.36 Kept: 74113
% 100.90/101.36 Inuse: 935
% 100.90/101.36 Deleted: 479
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 229502
% 100.90/101.36 Kept: 77407
% 100.90/101.36 Inuse: 940
% 100.90/101.36 Deleted: 479
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 240089
% 100.90/101.36 Kept: 79645
% 100.90/101.36 Inuse: 990
% 100.90/101.36 Deleted: 479
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36 Resimplifying clauses:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 248975
% 100.90/101.36 Kept: 81889
% 100.90/101.36 Inuse: 1025
% 100.90/101.36 Deleted: 584
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 254060
% 100.90/101.36 Kept: 84481
% 100.90/101.36 Inuse: 1035
% 100.90/101.36 Deleted: 584
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 265250
% 100.90/101.36 Kept: 89227
% 100.90/101.36 Inuse: 1055
% 100.90/101.36 Deleted: 584
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 271236
% 100.90/101.36 Kept: 91297
% 100.90/101.36 Inuse: 1065
% 100.90/101.36 Deleted: 584
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 285082
% 100.90/101.36 Kept: 96684
% 100.90/101.36 Inuse: 1095
% 100.90/101.36 Deleted: 584
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 294265
% 100.90/101.36 Kept: 100353
% 100.90/101.36 Inuse: 1115
% 100.90/101.36 Deleted: 584
% 100.90/101.36 Deletedinuse: 9
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36 Resimplifying clauses:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36 Resimplifying inuse:
% 100.90/101.36 Done
% 100.90/101.36
% 100.90/101.36 *** allocated 6568290 integers for clauses
% 100.90/101.36
% 100.90/101.36 Intermediate Status:
% 100.90/101.36 Generated: 303115
% 100.90/101.36 Kept: 102729
% 100.90/101.36 Inuse: 1145
% 100.90/101.36 Deleted: 690
% 218.17/218.61 Deletedinuse: 9
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 312070
% 218.17/218.61 Kept: 105355
% 218.17/218.61 Inuse: 1165
% 218.17/218.61 Deleted: 690
% 218.17/218.61 Deletedinuse: 9
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 323697
% 218.17/218.61 Kept: 109538
% 218.17/218.61 Inuse: 1195
% 218.17/218.61 Deleted: 690
% 218.17/218.61 Deletedinuse: 9
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61 *** allocated 4378860 integers for termspace/termends
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 333347
% 218.17/218.61 Kept: 111839
% 218.17/218.61 Inuse: 1235
% 218.17/218.61 Deleted: 690
% 218.17/218.61 Deletedinuse: 9
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 349995
% 218.17/218.61 Kept: 117975
% 218.17/218.61 Inuse: 1265
% 218.17/218.61 Deleted: 690
% 218.17/218.61 Deletedinuse: 9
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 363373
% 218.17/218.61 Kept: 121058
% 218.17/218.61 Inuse: 1290
% 218.17/218.61 Deleted: 690
% 218.17/218.61 Deletedinuse: 9
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61 Resimplifying clauses:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 370465
% 218.17/218.61 Kept: 123289
% 218.17/218.61 Inuse: 1305
% 218.17/218.61 Deleted: 1058
% 218.17/218.61 Deletedinuse: 10
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 378560
% 218.17/218.61 Kept: 125923
% 218.17/218.61 Inuse: 1325
% 218.17/218.61 Deleted: 1060
% 218.17/218.61 Deletedinuse: 12
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 385699
% 218.17/218.61 Kept: 128131
% 218.17/218.61 Inuse: 1335
% 218.17/218.61 Deleted: 1060
% 218.17/218.61 Deletedinuse: 12
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 394917
% 218.17/218.61 Kept: 130630
% 218.17/218.61 Inuse: 1350
% 218.17/218.61 Deleted: 1060
% 218.17/218.61 Deletedinuse: 12
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 412632
% 218.17/218.61 Kept: 134301
% 218.17/218.61 Inuse: 1380
% 218.17/218.61 Deleted: 1060
% 218.17/218.61 Deletedinuse: 12
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 424272
% 218.17/218.61 Kept: 136332
% 218.17/218.61 Inuse: 1416
% 218.17/218.61 Deleted: 1060
% 218.17/218.61 Deletedinuse: 12
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 433484
% 218.17/218.61 Kept: 138768
% 218.17/218.61 Inuse: 1425
% 218.17/218.61 Deleted: 1060
% 218.17/218.61 Deletedinuse: 12
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 444692
% 218.17/218.61 Kept: 140784
% 218.17/218.61 Inuse: 1448
% 218.17/218.61 Deleted: 1060
% 218.17/218.61 Deletedinuse: 12
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61 Resimplifying clauses:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 460046
% 218.17/218.61 Kept: 142809
% 218.17/218.61 Inuse: 1466
% 218.17/218.61 Deleted: 1451
% 218.17/218.61 Deletedinuse: 12
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 471296
% 218.17/218.61 Kept: 147110
% 218.17/218.61 Inuse: 1480
% 218.17/218.61 Deleted: 1453
% 218.17/218.61 Deletedinuse: 14
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 478495
% 218.17/218.61 Kept: 150839
% 218.17/218.61 Inuse: 1485
% 218.17/218.61 Deleted: 1453
% 218.17/218.61 Deletedinuse: 14
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 485671
% 218.17/218.61 Kept: 154589
% 218.17/218.61 Inuse: 1490
% 218.17/218.61 Deleted: 1453
% 218.17/218.61 Deletedinuse: 14
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 497439
% 218.17/218.61 Kept: 156641
% 218.17/218.61 Inuse: 1515
% 218.17/218.61 Deleted: 1453
% 218.17/218.61 Deletedinuse: 14
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61 *** allocated 9852435 integers for clauses
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 508620
% 218.17/218.61 Kept: 158745
% 218.17/218.61 Inuse: 1535
% 218.17/218.61 Deleted: 1459
% 218.17/218.61 Deletedinuse: 20
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 517891
% 218.17/218.61 Kept: 160774
% 218.17/218.61 Inuse: 1564
% 218.17/218.61 Deleted: 1459
% 218.17/218.61 Deletedinuse: 20
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61 Resimplifying clauses:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 523665
% 218.17/218.61 Kept: 162805
% 218.17/218.61 Inuse: 1583
% 218.17/218.61 Deleted: 2039
% 218.17/218.61 Deletedinuse: 20
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 533299
% 218.17/218.61 Kept: 165023
% 218.17/218.61 Inuse: 1615
% 218.17/218.61 Deleted: 2039
% 218.17/218.61 Deletedinuse: 20
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 544484
% 218.17/218.61 Kept: 169445
% 218.17/218.61 Inuse: 1640
% 218.17/218.61 Deleted: 2039
% 218.17/218.61 Deletedinuse: 20
% 218.17/218.61
% 218.17/218.61 Resimplifying inuse:
% 218.17/218.61 Done
% 218.17/218.61
% 218.17/218.61
% 218.17/218.61 Intermediate Status:
% 218.17/218.61 Generated: 549547
% 218.17/218.61 Kept: 172484
% 218.17/218.61 Inuse: 1Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------