TSTP Solution File: SWW283+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW283+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n019.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 23:21:49 EDT 2022
% Result : Timeout 300.06s 300.43s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWW283+1 : TPTP v8.1.0. Released v5.2.0.
% 0.10/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Sun Jun 5 18:21:25 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.96/1.55 *** allocated 10000 integers for termspace/termends
% 0.96/1.55 *** allocated 10000 integers for clauses
% 0.96/1.55 *** allocated 10000 integers for justifications
% 0.96/1.55 *** allocated 15000 integers for termspace/termends
% 0.96/1.55 *** allocated 22500 integers for termspace/termends
% 0.96/1.55 *** allocated 33750 integers for termspace/termends
% 0.96/1.55 Bliksem 1.12
% 0.96/1.55
% 0.96/1.55
% 0.96/1.55 Automatic Strategy Selection
% 0.96/1.55
% 0.96/1.55 *** allocated 50625 integers for termspace/termends
% 0.96/1.55 *** allocated 75937 integers for termspace/termends
% 0.96/1.55 *** allocated 113905 integers for termspace/termends
% 0.96/1.55
% 0.96/1.55 Clauses:
% 0.96/1.55
% 0.96/1.55 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) )
% 0.96/1.55 }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.96/1.55 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.96/1.55 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.96/1.55 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.96/1.55 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.55 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.55 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.96/1.55 X ), Z ), T ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T )
% 0.96/1.55 ) ) }.
% 0.96/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.96/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.96/1.55 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.96/1.55 .
% 0.96/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.96/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.96/1.55 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Nat_Onat ) }.
% 0.96/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.96/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.96/1.55 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.96/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( X ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) )
% 0.96/1.55 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), skol2( Z, Y ) ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.96/1.55 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = T, T =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), Y
% 0.96/1.55 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.96/1.55 tc_Complex_Ocomplex ) ), X ), T ) ) ) }.
% 0.96/1.55 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol2( X, Y ) ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.96/1.55 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = Z, Z =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), Y
% 0.96/1.55 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.96/1.55 tc_Complex_Ocomplex ) ), X ), Z ) ) ) }.
% 0.96/1.55 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.96/1.55 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.96/1.55 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.96/1.55 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.96/1.55 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.55 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), Y ), Y ) ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 0.96/1.55 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.55 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.96/1.55 }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 0.96/1.55 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), !
% 0.96/1.55 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ),
% 0.96/1.55 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.96/1.55 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.96/1.55 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.96/1.55 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 0.96/1.55 ) }.
% 0.96/1.55 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ), Z ), Y ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.96/1.55 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.96/1.55 }.
% 0.96/1.55 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.96/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ), hBOOL( hAPP(
% 0.96/1.55 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.96/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ) }.
% 0.96/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.96/1.55 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.96/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 0.96/1.55 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ), Y =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.96/1.55 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ), Y =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.55 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.96/1.55 ( tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, T, Z ) ), Y ) ),
% 0.96/1.55 alpha1( X, Y, T ) }.
% 0.96/1.55 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.96/1.55 ( tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, T, Z ) ), Y ) ),
% 0.96/1.55 alpha16( X, Y, Z, T ) }.
% 0.96/1.55 { ! class_Fields_Ofield( X ), ! alpha1( X, Y, T ), ! alpha16( X, Y, Z, T )
% 0.96/1.55 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.96/1.55 , c_Polynomial_Osmult( X, T, Z ) ), Y ) ) }.
% 0.96/1.55 { ! alpha16( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.96/1.55 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.96/1.55 ) ) }.
% 0.96/1.55 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha16( X, Y, Z, T ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.96/1.55 , Z ), Y ) ), alpha16( X, Y, Z, T ) }.
% 0.96/1.55 { ! alpha1( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.55 { Z = c_Groups_Ozero__class_Ozero( X ), alpha1( X, Y, Z ) }.
% 0.96/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha1( X
% 0.96/1.55 , Y, Z ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.96/1.55 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) )
% 0.96/1.55 , c_Polynomial_Odegree( X, Y ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), hBOOL(
% 0.96/1.55 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ),
% 0.96/1.55 c_Polynomial_Osmult( X, T, Y ) ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult
% 0.96/1.55 ( X, T, Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.96/1.55 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.55 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.55 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.55 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.55 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.55 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP
% 0.96/1.55 ( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.96/1.55 ( X ), T ), Z ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y
% 0.96/1.55 ) ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ), hBOOL( hAPP( hAPP
% 0.96/1.55 ( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.96/1.55 ( X ), Z ), U ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T
% 0.96/1.55 ) ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.96/1.55 X ), T ), Z ) ), Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.96/1.55 , U, Z ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), T ), U ) ), Y ) ) }.
% 0.96/1.55 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 0.96/1.55 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 0.96/1.55 c_Polynomial_Osmult( X, Y, Z ) ) ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Z ) ) }.
% 0.96/1.55 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 0.96/1.55 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 0.96/1.55 Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.96/1.55 X ) ), T ), c_Polynomial_Osmult( X, Y, Z ) ) ) }.
% 0.96/1.55 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.96/1.55 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), T = c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.96/1.55 X ) ), c_Polynomial_Osmult( X, T, Z ) ), Y ) ) }.
% 0.96/1.55 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.96/1.55 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Osmult( X, Z, Y ) ) ), Z
% 0.96/1.55 = c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.55 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.55 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.55 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.96/1.55 c_Polynomial_Odegree( X, Y ) }.
% 0.96/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.96/1.55 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), X ) ) }
% 0.96/1.55 .
% 0.96/1.55 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.96/1.55 , Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ),
% 0.96/1.55 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ),
% 0.96/1.55 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 0.96/1.55 c_Polynomial_Odegree( X, Y ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.96/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Orderings_Oord__class_Oless__eq
% 0.96/1.55 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 0.96/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.55 c_Polynomial_Odegree( X, Z ) ), Y ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.96/1.55 X ) ) }.
% 0.96/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.96/1.55 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.55 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.55 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.55 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.96/1.55 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.96/1.55 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.55 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.96/1.55 .
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.96/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.96/1.55 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.96/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.96/1.55 ), X ) ) }.
% 0.96/1.55 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.96/1.55 = Y }.
% 0.96/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.96/1.55 = Y }.
% 0.96/1.55 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.96/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.55 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.96/1.55 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.96/1.55 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.96/1.55 = Y }.
% 0.96/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.96/1.55 = Y }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.96/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.55 Y ) }.
% 0.96/1.55 { ! X = c_Nat_OSuc( X ) }.
% 0.96/1.55 { ! c_Nat_OSuc( X ) = X }.
% 0.96/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.96/1.55 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.55 Y ), ! Z = Y }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.55 Z ), ! Z = Y }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.55 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.55 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.96/1.55 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.55 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.55 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.96/1.55 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.96/1.55 , Y ), X ) }.
% 0.96/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.96/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.96/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.55 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.55 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.96/1.55 }.
% 0.96/1.55 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.96/1.55 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.96/1.55 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.96/1.55 X ) ) }.
% 0.96/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.96/1.55 tc_Nat_Onat ) }.
% 0.96/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.96/1.55 tc_Nat_Onat ) }.
% 0.96/1.55 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.96/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.96/1.55 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.55 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.96/1.55 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.55 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.55 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.96/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.96/1.55 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.96/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.96/1.55 ), X ) ) }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.55 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.55 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.96/1.55 .
% 0.96/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.96/1.55 .
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.96/1.55 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.55 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.55 , ! Z = Y }.
% 0.96/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.55 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.55 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.55 , ! Z = Y }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.55 , ! Y = Z }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.96/1.55 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.96/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.55 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.55 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.55 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.96/1.55 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.96/1.55 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.96/1.55 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.96/1.55 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.55 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.55 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.55 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.96/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.55 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.96/1.55 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.55 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.55 { alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.96/1.55 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.96/1.55 { alpha28( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.96/1.55 ( X, Y ), Z ) ) }.
% 0.96/1.55 { ! alpha28( X, Y, Z ), alpha31( X, Y, Z ), Z = Y }.
% 0.96/1.55 { ! alpha28( X, Y, Z ), alpha31( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.96/1.55 ) ) }.
% 0.96/1.55 { ! alpha31( X, Y, Z ), alpha28( X, Y, Z ) }.
% 0.96/1.55 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha28( X, Y, Z ) }.
% 0.96/1.55 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.96/1.55 }.
% 0.96/1.55 { ! alpha31( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.96/1.55 X, Y ), Z ) ), alpha31( X, Y, Z ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.55 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.96/1.55 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.96/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.96/1.55 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.96/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.96/1.55 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.96/1.55 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.55 X, Y, Z ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Nat_Onat ), Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.96/1.55 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Nat_Onat ), Z ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.96/1.55 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.96/1.55 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.96/1.55 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.55 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.96/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha2( X, Y ) }.
% 0.96/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.55 { ! alpha2( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.96/1.55 c_Nat_OSuc( X ) ) }.
% 0.96/1.55 { ! alpha2( X, Y ), Y = c_Nat_OSuc( skol3( Z, Y ) ) }.
% 0.96/1.55 { ! alpha2( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol3( X, Y
% 0.96/1.55 ), X ) }.
% 0.96/1.55 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.96/1.55 ), alpha2( X, Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.96/1.55 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.96/1.55 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.55 Y ), X ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol4( X ) ) }.
% 0.96/1.55 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.96/1.55 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.55 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.55 Y ), X ) ), X ) ), Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.96/1.55 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ), X ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.55 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.55 X ), Y ) ), X ) ), Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.96/1.55 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha3( X, Y, Z, T ),
% 0.96/1.55 alpha17( X, Y, Z, T ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z, T ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha17( X, Y, Z, T ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.55 { ! alpha17( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.55 { ! alpha17( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.55 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha17( X, Y, Z, T ) }.
% 0.96/1.55 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.96/1.55 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.55 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha3( X, Y, Z, T ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha4( X, Y, Z, T ),
% 0.96/1.55 alpha18( X, Y, Z, T ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha18( X, Y, Z, T ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.55 { ! alpha18( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.55 { ! alpha18( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.55 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha18( X, Y, Z, T ) }.
% 0.96/1.55 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.96/1.55 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.96/1.55 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha4( X, Y, Z, T ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.55 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.55 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.96/1.55 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.55 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.55 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.55 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.55 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( X ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.55 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.55 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( X ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.96/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.96/1.55 .
% 0.96/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.96/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.96/1.55 .
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.55 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.55 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.96/1.55 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.55 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.55 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( X ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.55 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.55 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.96/1.55 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.96/1.55 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.96/1.55 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.96/1.55 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.96/1.55 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.96/1.55 .
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.96/1.55 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.55 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.96/1.55 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.96/1.55 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.55 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.55 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.55 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.55 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.55 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.55 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.55 , ! Z = Y }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.55 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.55 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.55 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.55 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.55 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.55 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.96/1.55 ( X, Z, Y ) }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.55 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.55 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.55 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.55 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.55 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.55 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.55 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.55 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.55 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.55 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.55 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.55 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.55 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.55 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.55 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.55 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.96/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.96/1.55 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.96/1.55 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.96/1.55 ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.96/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.96/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.96/1.55 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.96/1.55 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.96/1.55 c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.55 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.96/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.96/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.96/1.55 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.96/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.96/1.55 .
% 0.96/1.55 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.96/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.96/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.96/1.55 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.96/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.96/1.55 .
% 0.96/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Nat_Onat ), X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.96/1.55 .
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Nat_Onat ), X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.96/1.55 .
% 0.96/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.96/1.55 ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.55 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.96/1.55 , c_Nat_OSuc( X ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.96/1.55 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.96/1.55 }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.96/1.55 c_Nat_OSuc( X ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.96/1.55 ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.96/1.55 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.96/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X =
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.55 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone(
% 0.96/1.55 tc_Nat_Onat ) ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.96/1.55 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Nat_Onat ), Z ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.55 tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.96/1.55 ) }.
% 0.96/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.96/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.96/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.96/1.55 ) }.
% 0.96/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.96/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.96/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.55 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.96/1.55 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.55 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.55 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.96/1.55 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.55 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.96/1.55 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.55 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.55 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.96/1.55 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.96/1.55 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.55 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.55 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.55 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.55 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.96/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.96/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.96/1.55 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.55 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.55 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.55 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.96/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.55 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.55 ( X ), T ), Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 0.96/1.55 ), Z ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.55 ( X ), Z ), T ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 0.96/1.55 ), Z ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.55 ( X ), Y ), T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z
% 0.96/1.55 ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), U ), T ) ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.55 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T
% 0.96/1.55 ) ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.96/1.55 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), c_Groups_Oone__class_Oone( X ) ), Y ) ) }
% 0.96/1.55 .
% 0.96/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.96/1.55 = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.96/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.96/1.55 tc_Nat_Onat ) ) = Y }.
% 0.96/1.55 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.96/1.55 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 0.96/1.55 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.96/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.96/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.55 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hBOOL(
% 0.96/1.55 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.96/1.55 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X
% 0.96/1.55 ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.55 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), hBOOL( hAPP
% 0.96/1.55 ( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.96/1.55 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.96/1.55 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ) ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.96/1.55 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.96/1.55 ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.55 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.96/1.55 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha5( X, Y
% 0.96/1.55 , Z ), alpha19( X, Y, Z ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha19( X, Y, Z ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.55 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.55 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.96/1.55 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) ), alpha19( X, Y, Z ) }.
% 0.96/1.55 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.96/1.55 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.55 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), Y ), alpha5( X, Y, Z ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( X ) ), alpha6( X, Y, Z ), alpha20( X, Y, Z ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( X ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha20( X, Y, Z ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( X ) ) }.
% 0.96/1.55 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.55 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.96/1.55 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( X ), Y ), alpha20( X, Y, Z ) }.
% 0.96/1.55 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.96/1.55 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.55 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) ), alpha6( X, Y, Z ) }.
% 0.96/1.55 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.55 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.55 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.55 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( X ) ) }.
% 0.96/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.55 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.96/1.55 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.55 { ! class_Rings_Oordered__semiring( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.55 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.55 { ! class_Rings_Oordered__semiring( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.55 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.96/1.55 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.55 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.96/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.55 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.96/1.55 { ! class_Rings_Oordered__semiring( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.55 { ! class_Rings_Oordered__semiring( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.55 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.96/1.55 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.55 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.96/1.55 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.55 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( X ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.55 c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.55 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.55 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.55 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.55 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 0.96/1.55 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), T =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.96/1.55 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.96/1.55 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.55 X ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 0.96/1.55 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.96/1.55 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.55 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 0.96/1.55 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), Z =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), T ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.96/1.55 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.96/1.55 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.55 X ), T ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 0.96/1.55 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.96/1.55 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.55 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.96/1.55 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.96/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.55 tc_Nat_Onat ), Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.55 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.55 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.96/1.55 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.96/1.55 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.96/1.55 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.96/1.55 ), X ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.96/1.55 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.96/1.55 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.55 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.96/1.55 , Y ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 X ), Y ), Z = Y }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.55 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.55 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.96/1.55 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.55 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.55 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.55 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.55 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.96/1.55 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.96/1.55 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.96/1.55 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.96/1.55 hAPP( Y, U ) ) }.
% 0.96/1.55 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.96/1.55 ( Z, skol5( X, Y, Z ) ), hAPP( Y, skol5( X, Y, Z ) ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.55 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.96/1.55 ( X, Z, Y ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.96/1.55 ( X, Y, Z ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.55 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.96/1.55 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.55 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.96/1.55 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.96/1.55 hAPP( Y, U ) ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.55 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.55 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.55 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.55 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.96/1.55 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.96/1.55 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.55 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.55 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.96/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.55 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.55 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.55 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.96/1.55 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.96/1.55 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.96/1.55 hAPP( Y, U ) ) }.
% 0.96/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.55 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.55 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.96/1.55 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.96/1.55 ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.55 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.96/1.55 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.96/1.55 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.96/1.55 ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.55 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.96/1.55 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.96/1.55 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.96/1.55 ) ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.55 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.96/1.55 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.96/1.55 ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.55 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.96/1.55 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.96/1.55 ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.55 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.96/1.55 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.96/1.55 ) ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.55 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.96/1.55 ), Z ) ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.55 , ! X = Z, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.96/1.55 Z ), Y ) ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.55 , ! X = Y }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.55 , ! Y = X }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.55 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.96/1.55 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.96/1.55 ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.55 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.55 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.96/1.55 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.96/1.55 ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.55 , ! Y = X }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.96/1.55 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.96/1.55 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.96/1.55 ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.96/1.55 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.96/1.55 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.96/1.55 ) ) }.
% 0.96/1.55 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.96/1.55 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.96/1.55 ), X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.96/1.55 ), Z ) ) }.
% 0.96/1.55 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.96/1.55 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.96/1.55 ), X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.96/1.55 Z ), Y ) ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.96/1.55 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.96/1.55 ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.96/1.55 ), Y = X }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.96/1.55 ), Y = X }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.96/1.55 ), Z ) ) }.
% 0.96/1.55 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.96/1.55 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.96/1.55 ), Z ) ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.96/1.55 , X ) ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.96/1.55 ), Y ) ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , Y = X }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.96/1.55 ), Y = X }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.96/1.55 ), X = Y }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , ! X = Y, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.96/1.55 ), Y ) ) }.
% 0.96/1.55 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.96/1.55 , X ) ) }.
% 0.96/1.55 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.96/1.55 , X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.96/1.55 , X ) ) }.
% 0.96/1.55 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.96/1.55 , X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.96/1.55 ), Y ) ) }.
% 0.96/1.55 { ! alpha7( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.55 tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.55 { ! alpha7( X, Y ), ! Y = X }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , Y = X, alpha7( X, Y ) }.
% 0.96/1.55 { ! alpha7( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.55 tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.55 { ! alpha7( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.55 tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.55 , alpha7( X, Y ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , alpha8( X, Y ), Y = X }.
% 0.96/1.55 { ! alpha8( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.55 tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.55 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.96/1.55 , X ) ) }.
% 0.96/1.55 { ! alpha8( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.55 tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.55 { ! alpha8( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.55 tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.96/1.55 , alpha8( X, Y ) }.
% 0.96/1.55 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.96/1.55 , X ) ) }.
% 0.96/1.55 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X )
% 0.96/1.55 , Y ) ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.96/1.55 ), Y = X }.
% 0.96/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.96/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.96/1.55 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.96/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.96/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.96/1.55 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.55 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.55 X ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 0.96/1.55 , Y ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.96/1.55 ), Y ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.55 tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.55 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.55 X ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 0.96/1.55 , Y ) ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.96/1.55 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Nat_Onat ), Y ) }.
% 0.96/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.96/1.55 ), X ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.96/1.55 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), Z =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.55 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.96/1.55 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.96/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.96/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.96/1.55 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.55 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.55 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.55 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.55 tc_Nat_Onat ), X ), Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.96/1.55 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.96/1.55 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.96/1.55 .
% 0.96/1.55 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.96/1.55 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.96/1.55 }.
% 0.96/1.55 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.96/1.55 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.96/1.55 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.96/1.55 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 0.96/1.55 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 0.96/1.55 .
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.96/1.55 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 0.96/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 0.96/1.55 ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.96/1.55 tc_Nat_Onat ) ) = Y }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.96/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.96/1.55 = Y }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.96/1.55 = Y }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.96/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.96/1.55 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.96/1.55 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.96/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.96/1.55 .
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.96/1.55 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.96/1.55 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.96/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.96/1.55 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.96/1.55 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Opcompose( X, Z, Y )
% 0.96/1.55 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.55 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.55 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.96/1.55 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.96/1.55 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.96/1.55 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.96/1.55 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.96/1.55 ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP( hAPP
% 0.96/1.55 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ), X = Y }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.96/1.55 , ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.96/1.55 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X
% 0.96/1.55 ) ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 0.96/1.55 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), Z =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.96/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.96/1.55 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 0.96/1.55 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 0.96/1.55 X, Z ), Y ) ) }.
% 0.96/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.96/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.96/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Int_Oint ), X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.96/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.96/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.96/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.96/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.96/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.96/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.96/1.55 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.96/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.96/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.96/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.96/1.55 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.55 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.55 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.96/1.55 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.55 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.96/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.96/1.55 ( tc_Int_Oint ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.96/1.55 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.96/1.55 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.55 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.55 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.96/1.55 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.96/1.55 , c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Z, Y ) ), Y ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.55 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.96/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 0.96/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ), hBOOL( hAPP(
% 0.96/1.55 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.96/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Int_Oint ) ) }.
% 0.96/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.96/1.55 tc_Int_Oint ) ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.96/1.55 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), ! hAPP(
% 0.96/1.55 c_Polynomial_Ocoeff( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 0.96/1.55 , Y ) }.
% 0.96/1.55 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.55 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.96/1.55 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.96/1.55 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.96/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.96/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Omono( tc_Nat_Onat, X
% 0.96/1.55 , c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), T ), Z ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 0.96/1.55 ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.55 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.96/1.55 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) ) }.
% 0.96/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.55 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 0.96/1.55 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol6( X
% 0.96/1.55 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol6( X, Y, Z ) ), Z = Y
% 0.96/1.55 }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 0.96/1.55 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 0.96/1.55 c_Polynomial_Ocoeff( X, Y ) }.
% 0.96/1.55 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.96/1.55 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 0.96/1.55 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.96/1.55 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.96/1.55 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.96/1.55 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.96/1.55 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.96/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.96/1.55 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.55 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.55 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.96/1.55 T ) ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.96/1.55 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.96/1.55 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.96/1.55 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.96/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.96/1.55 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.96/1.55 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.96/1.55 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.96/1.55 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.96/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.96/1.55 ) }.
% 0.96/1.55 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.96/1.55 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.96/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.96/1.55 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.96/1.55 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.96/1.55 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.55 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.96/1.55 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.55 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.96/1.55 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.96/1.55 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.96/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.96/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.96/1.55 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 0.96/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.55 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.96/1.55 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.96/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.55 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.96/1.55 ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.55 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.96/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.55 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.96/1.55 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.55 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.96/1.55 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.96/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.96/1.55 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.96/1.55 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.55 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( X ) ) }.
% 0.96/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.96/1.55 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.96/1.55 , Z, Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.55 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.96/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.55 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.96/1.55 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.96/1.55 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.55 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.96/1.55 ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.55 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.96/1.55 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.55 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.96/1.55 ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ),
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), ! hBOOL( hAPP(
% 0.96/1.55 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), hBOOL( hAPP( hAPP
% 0.96/1.55 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ),
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), ! hBOOL( hAPP(
% 0.96/1.55 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), hBOOL( hAPP( hAPP
% 0.96/1.55 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.96/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.96/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.55 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.55 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 0.96/1.55 ), Y ) ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.55 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.55 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.55 }.
% 0.96/1.55 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.96/1.55 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.55 c_Polynomial_Odegree( X, Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), ! hBOOL
% 0.96/1.55 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Y ),
% 0.96/1.55 Z ) ), Z = Y }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.96/1.55 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.96/1.55 ) ) = X }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.55 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 0.96/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.96/1.55 tc_Nat_Onat, Y, c_Polynomial_Odegree( X, Z ) ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.55 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.55 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.55 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.96/1.55 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 0.96/1.55 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 0.96/1.55 tc_Nat_Onat ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.96/1.55 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.96/1.55 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.96/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.55 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.96/1.55 ( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 0.96/1.55 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.96/1.55 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.96/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.55 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.96/1.55 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.96/1.55 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.55 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.96/1.55 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 0.96/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.55 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 0.96/1.55 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.96/1.55 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.55 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.55 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.96/1.55 , skol7( T, U, Z ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.55 c_Polynomial_Odegree( X, Y ), Z ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ), skol7( X
% 0.96/1.55 , Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.96/1.55 Y ), Z ) }.
% 0.96/1.55 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) ), ! hBOOL( hAPP(
% 0.96/1.55 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ), hBOOL( hAPP(
% 0.96/1.55 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.96/1.55 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.96/1.55 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.55 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.96/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.55 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.96/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.55 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.96/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.96/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.96/1.55 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.96/1.55 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.55 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.96/1.55 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.96/1.55 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 0.96/1.55 }.
% 0.96/1.55 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.55 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.96/1.55 T ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.55 c_Polynomial_Odegree( X, c_Groups_Ominus__class_Ominus(
% 0.96/1.55 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 0.96/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.96/1.55 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.96/1.55 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.96/1.55 .
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.96/1.55 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.96/1.55 tc_Int_Oint, X, Y ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.96/1.55 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.96/1.55 .
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.96/1.55 ( tc_Int_Oint ) ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.96/1.55 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.96/1.55 tc_Int_Oint, X, Y ) }.
% 0.96/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.96/1.55 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.96/1.55 ) }.
% 0.96/1.55 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.55 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.96/1.55 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.55 }.
% 0.96/1.55 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.55 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.96/1.55 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.96/1.55 .
% 0.96/1.55 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.55 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.96/1.55 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.96/1.55 .
% 0.96/1.55 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.55 Z, c_Polynomial_Odegree( X, Y ) ), c_Orderings_Oord__class_Oless(
% 0.96/1.55 tc_Nat_Onat, Z, skol8( T, U, Z ) ) }.
% 0.96/1.55 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.55 Z, c_Polynomial_Odegree( X, Y ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.96/1.55 skol8( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.96/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) = c_Nat_OSuc(
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.96/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 0.96/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol9( Z, Y ) ) ), !
% 0.96/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.96/1.55 , hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, U, hAPP(
% 0.96/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.96/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.55 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.96/1.55 tc_Int_Oint, skol9( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.96/1.55 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.96/1.55 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.96/1.55 tc_Int_Oint, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.96/1.55 , Z ), X ) ) ) ) }.
% 0.96/1.55 { ! class_Fields_Ofield( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) ), Z ) ) }
% 0.96/1.55 .
% 0.96/1.55 { ! class_Fields_Ofield( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.55 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) ), Y ) ) }
% 0.96/1.55 .
% 0.96/1.55 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ) =
% 0.96/1.55 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.96/1.55 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.96/1.55 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.96/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Int_Onumber( X ), ! c_Int_Onumber__class_Onumber__of( X, Z ) = Y
% 0.96/1.56 , Y = c_Int_Onumber__class_Onumber__of( X, Z ) }.
% 0.96/1.56 { ! class_Int_Onumber( X ), ! Y = c_Int_Onumber__class_Onumber__of( X, Z )
% 0.96/1.56 , c_Int_Onumber__class_Onumber__of( X, Z ) = Y }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), !
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, Y ), Z = Y }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), ! Z = Y
% 0.96/1.56 , c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.96/1.56 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 0.96/1.56 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 0.96/1.56 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.96/1.56 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 0.96/1.56 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.96/1.56 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Opoly__gcd( X, Z, Y ) ) )
% 0.96/1.56 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.96/1.56 , T ), Z ) ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.96/1.56 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Opoly__gcd( X, Z, Y ) ) )
% 0.96/1.56 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.96/1.56 , T ), Y ) ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.96/1.56 ( tc_Polynomial_Opoly( X ) ), T ), Z ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Y ) ), hBOOL(
% 0.96/1.56 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 0.96/1.56 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.96/1.56 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), T ) ), hBOOL(
% 0.96/1.56 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ),
% 0.96/1.56 c_Polynomial_Opoly__gcd( X, Y, T ) ) ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.96/1.56 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.56 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.96/1.56 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.96/1.56 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.96/1.56 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.96/1.56 ), c_Int_Onumber__class_Onumber__of( X, Z ) ) }.
% 0.96/1.56 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.96/1.56 ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.96/1.56 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.96/1.56 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.96/1.56 Z ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.96/1.56 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.96/1.56 ( X, Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.96/1.56 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.56 T ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.96/1.56 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.56 T ) ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.96/1.56 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.96/1.56 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.96/1.56 ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.96/1.56 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), c_Int_Onumber__class_Onumber__of( X, T ) ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.56 Z ) ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), Z ) ) ), Y ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X, hAPP
% 0.96/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) = hAPP(
% 0.96/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.96/1.56 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.96/1.56 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.96/1.56 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.96/1.56 .
% 0.96/1.56 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.96/1.56 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.96/1.56 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), ! c_Int_Onumber__class_Onumber__of(
% 0.96/1.56 tc_Nat_Onat, Y ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.56 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.96/1.56 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.96/1.56 , ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.96/1.56 ( tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.96/1.56 , Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.96/1.56 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.96/1.56 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.96/1.56 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 0.96/1.56 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), !
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.56 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.96/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.56 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.56 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.96/1.56 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), alpha32( X, Y, Z, T ), ! Y =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.96/1.56 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.96/1.56 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), alpha32( X, Y, Z, T ), ! hAPP(
% 0.96/1.56 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.96/1.56 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 0.96/1.56 .
% 0.96/1.56 { ! alpha32( X, Y, Z, T ), alpha33( X, Y, Z, T ), alpha29( X, Y, T ) }.
% 0.96/1.56 { ! alpha32( X, Y, Z, T ), alpha33( X, Y, Z, T ), ! hAPP(
% 0.96/1.56 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! alpha33( X, Y, Z, T ), alpha32( X, Y, Z, T ) }.
% 0.96/1.56 { ! alpha29( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.96/1.56 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.56 alpha32( X, Y, Z, T ) }.
% 0.96/1.56 { ! alpha33( X, Y, Z, T ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ), Z ), T ) ), alpha34( X, Y, Z, T ) }.
% 0.96/1.56 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ),
% 0.96/1.56 Z ), T ) ), alpha33( X, Y, Z, T ) }.
% 0.96/1.56 { ! alpha34( X, Y, Z, T ), alpha33( X, Y, Z, T ) }.
% 0.96/1.56 { ! alpha34( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ), skol10( X, Y, U, W ) ), Y ) ) }.
% 0.96/1.56 { ! alpha34( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ), skol10( X, Y, U, T ) ), T ) ) }.
% 0.96/1.56 { ! alpha34( X, Y, Z, T ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ), skol10( X, Y, Z, T ) ), Z ) ) }.
% 0.96/1.56 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.96/1.56 , U ), Y ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ), U ), T ) ), hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), U ), Z ) ), alpha34
% 0.96/1.56 ( X, Y, Z, T ) }.
% 0.96/1.56 { ! alpha29( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! alpha29( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha29( X, Y, Z
% 0.96/1.56 ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, c_Int_OPls ), hAPP( hAPP
% 0.96/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ) ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ), X ) ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, c_Int_OPls ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ) ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ), X ) ) = hAPP( hAPP
% 0.96/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) ), X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ), hAPP( hAPP
% 0.96/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.96/1.56 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 0.96/1.56 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 0.96/1.56 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Int_OPls ) = X }.
% 0.96/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) ) }.
% 0.96/1.56 { c_Groups_Ozero__class_Ozero( tc_Int_Oint ) =
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.96/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OPls ) }
% 0.96/1.56 .
% 0.96/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OPls )
% 0.96/1.56 }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.96/1.56 { c_Int_OPls = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.56 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.56 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 0.96/1.56 = Y }.
% 0.96/1.56 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.56 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( X ) }.
% 0.96/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 0.96/1.56 X, Y ) ) = Y }.
% 0.96/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.96/1.56 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.96/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.96/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.56 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 0.96/1.56 ) ), Y ) }.
% 0.96/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.96/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.96/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 0.96/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.56 , Y ) ) = Y }.
% 0.96/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Int_OPls ), X
% 0.96/1.56 ) = c_Int_OPls }.
% 0.96/1.56 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.96/1.56 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 0.96/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 0.96/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.56 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 0.96/1.56 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 0.96/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.96/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.96/1.56 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.96/1.56 ) ), Z ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.56 c_Int_OPls ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) }.
% 0.96/1.56 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.56 { c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 0.96/1.56 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.96/1.56 Y ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.96/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.96/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 0.96/1.56 ) }.
% 0.96/1.56 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) }.
% 0.96/1.56 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ), alpha9( X, Y ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.96/1.56 { ! alpha9( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.96/1.56 { ! alpha9( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.96/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha9( X, Y ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ), alpha9( X
% 0.96/1.56 , Y ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, Y ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, Y ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.96/1.56 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.96/1.56 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.56 ( tc_Int_Oint, c_Int_OPls, Y ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, Y ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.96/1.56 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.96/1.56 tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.96/1.56 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.96/1.56 }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.56 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 0.96/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 0.96/1.56 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.96/1.56 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.96/1.56 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.96/1.56 X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.56 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.96/1.56 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.96/1.56 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.56 { c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) = X }.
% 0.96/1.56 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.96/1.56 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.56 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 0.96/1.56 , Y = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.56 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 0.96/1.56 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 0.96/1.56 = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.56 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.56 ) ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.56 ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.96/1.56 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.56 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.56 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.56 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.96/1.56 .
% 0.96/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.56 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.56 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.56 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.96/1.56 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( X ) ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.56 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.56 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.96/1.56 .
% 0.96/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.56 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.56 , Y ) ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.96/1.56 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.96/1.56 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.96/1.56 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.56 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.56 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.56 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.56 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.96/1.56 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 0.96/1.56 , Y ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.96/1.56 ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.96/1.56 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse
% 0.96/1.56 ( X, Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.56 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.56 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.56 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 0.96/1.56 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.96/1.56 ) ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.96/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.96/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.96/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 0.96/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Nat_Onat ) }.
% 0.96/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.96/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 0.96/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_Opred( X ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ),
% 0.96/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.96/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_Opred( X ) ) ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 0.96/1.56 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 0.96/1.56 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 0.96/1.56 c_Polynomial_Opoly__gcd( X, Z, c_Divides_Odiv__class_Omod(
% 0.96/1.56 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.96/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 0.96/1.56 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Omod(
% 0.96/1.56 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T,
% 0.96/1.56 c_Polynomial_Osmult( X, Y, Z ) ) = c_Divides_Odiv__class_Omod(
% 0.96/1.56 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.96/1.56 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.96/1.56 c_Polynomial_Opoly__gcd( X, Y, c_Divides_Odiv__class_Omod(
% 0.96/1.56 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_Opred( Y ), X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_Opred( Y ), X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.96/1.56 { c_Int_Opred( X ) = c_Groups_Ominus__class_Ominus( tc_Int_Oint, X,
% 0.96/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 0.96/1.56 tc_Polynomial_Opoly( X ), Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.56 c_Polynomial_Odegree( X, c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.96/1.56 ( X ), Z, Y ) ), c_Polynomial_Odegree( X, Y ) ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), ! class_Int_Onumber( X ), ! hBOOL(
% 0.96/1.56 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) ) ), c_Divides_Odiv__class_Omod
% 0.96/1.56 ( X, c_Int_Onumber__class_Onumber__of( X, Y ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, Z ) ) = c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( X ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), ! class_Int_Onumber( X ), !
% 0.96/1.56 c_Divides_Odiv__class_Omod( X, c_Int_Onumber__class_Onumber__of( X, Y ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, Z ) ) = c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 0.96/1.56 , Y, Z ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 0.96/1.56 , Y, Z ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 0.96/1.56 Z ) = c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.96/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.96/1.56 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ), X ), Y ) =
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.96/1.56 tc_Int_Oint, Z, X ), Y ) }.
% 0.96/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.96/1.56 tc_Int_Oint, Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.96/1.56 tc_Int_Oint, Z, Y ), X ) }.
% 0.96/1.56 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) =
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.96/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, X ) ) ) }.
% 0.96/1.56 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.96/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, X ) ) ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) =
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) =
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.96/1.56 tc_Nat_Onat, X, Y ), Y ) }.
% 0.96/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.96/1.56 tc_Nat_Onat, Y, X ), X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.96/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.96/1.56 tc_Nat_Onat, Y, X ), X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.96/1.56 tc_Int_Oint, X, Y ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.96/1.56 ( tc_Int_Oint, Y, X ) ) }.
% 0.96/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), Y ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.96/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 0.96/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 0.96/1.56 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 0.96/1.56 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.96/1.56 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), Z )
% 0.96/1.56 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) ) }.
% 0.96/1.56 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! hBOOL( hAPP( hAPP
% 0.96/1.56 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ), hBOOL( hAPP( hAPP
% 0.96/1.56 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.96/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.96/1.56 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 0.96/1.56 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 0.96/1.56 }.
% 0.96/1.56 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol11( X, Y ) ) }.
% 0.96/1.56 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 0.96/1.56 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.56 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol12( X, Y ) ) }.
% 0.96/1.56 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 0.96/1.56 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.56 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.56 { ! c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.56 { c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.96/1.56 c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.96/1.56 tc_Int_Oint, Y, X ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.96/1.56 tc_Int_Oint, Y, X ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.96/1.56 ( tc_Int_Oint, Y, X ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.96/1.56 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Int_Onumber__class_Onumber__of
% 0.96/1.56 ( tc_Int_Oint, X ), c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) )
% 0.96/1.56 = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.56 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), c_Int_Onumber__class_Onumber__of
% 0.96/1.56 ( tc_Int_Oint, Y ) ), c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X )
% 0.96/1.56 ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.96/1.56 tc_Nat_Onat ), X ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X )
% 0.96/1.56 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.56 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 0.96/1.56 X, Z, Y ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.96/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.96/1.56 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.96/1.56 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 0.96/1.56 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.96/1.56 ), Z ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 0.96/1.56 , Y ) ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.96/1.56 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.96/1.56 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.96/1.56 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.96/1.56 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.56 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.96/1.56 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.96/1.56 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.96/1.56 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.56 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.96/1.56 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.96/1.56 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 0.96/1.56 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.56 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.96/1.56 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.96/1.56 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 0.96/1.56 Y ) ), Y ) }.
% 0.96/1.56 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.96/1.56 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 0.96/1.56 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 0.96/1.56 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 0.96/1.56 , U ), Z ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.96/1.56 ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), T ), Y ) ),
% 0.96/1.56 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), T ), Z ) ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, Y, T )
% 0.96/1.56 ) ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 0.96/1.56 , c_Divides_Odiv__class_Omod( X, T, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.96/1.56 ( X, T, Z ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.96/1.56 ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.96/1.56 ) ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.96/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.96/1.56 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 0.96/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 0.96/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.56 skol13( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, skol13( X, T, U ),
% 0.96/1.56 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.96/1.56 , Y ) }.
% 0.96/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), skol13( X, Y, Z ) ), Z ), Y ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.96/1.56 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( X, c_Int_Onumber__class_Onumber__of(
% 0.96/1.56 tc_Nat_Onat, Y ) ) = c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.96/1.56 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( X, c_Int_Onumber__class_Onumber__of(
% 0.96/1.56 tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Int_Oint ) ) = X }.
% 0.96/1.56 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.96/1.56 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.56 { c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) }.
% 0.96/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) =
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.96/1.56 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), c_Divides_Odiv__class_Odiv( X, Y, Z ) ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( X, T, Z ) ) ), hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), c_Divides_Odiv__class_Odiv( X, Y, Z ) ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( X, T, Z ) ) ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.56 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat( X,
% 0.96/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) =
% 0.96/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( X, Z ) ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) }.
% 0.96/1.56 { ! class_Nat_Osemiring__char__0( X ), ! c_Nat_Osemiring__1__class_Oof__nat
% 0.96/1.56 ( X, Z ) = c_Nat_Osemiring__1__class_Oof__nat( X, Y ), Z = Y }.
% 0.96/1.56 { ! class_Nat_Osemiring__char__0( X ), ! Z = Y,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( X, Z ) =
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( X, Y ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Nat_Osemiring__1__class_Oof__nat
% 0.96/1.56 ( X, Z ), c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__semidom( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Nat_Osemiring__1__class_Oof__nat
% 0.96/1.56 ( X, Z ), c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.56 ( X, c_Nat_Osemiring__1__class_Oof__nat( X, Z ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.56 ( tc_Nat_Onat, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( X, Z ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.56 ( X, c_Nat_Osemiring__1__class_Oof__nat( X, Z ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.56 ( tc_Nat_Onat, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( X, Z ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) }.
% 0.96/1.56 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat( X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.56 ( X, c_Nat_Osemiring__1__class_Oof__nat( X, Y ),
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__semidom( X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__semidom( X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) }.
% 0.96/1.56 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat( X,
% 0.96/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X
% 0.96/1.56 ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.56 tc_Int_Oint, X, Y ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.96/1.56 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.96/1.56 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Int_Oint ), Y ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 0.96/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.56 { c_Groups_Ozero__class_Ozero( tc_Int_Oint ) =
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.56 { c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.56 { ! c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), ! hBOOL( hAPP( X, Y ) )
% 0.96/1.56 , hBOOL( hAPP( X, c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, skol14
% 0.96/1.56 ( X ) ) ) ) }.
% 0.96/1.56 { ! hBOOL( hAPP( X, c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) )
% 0.96/1.56 ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol22( Z ) ) }.
% 0.96/1.56 { ! hBOOL( hAPP( X, c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) )
% 0.96/1.56 ), hBOOL( hAPP( X, skol22( X ) ) ) }.
% 0.96/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol15( Y ) ), hBOOL( hAPP( X
% 0.96/1.56 , c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Z ) ) ) }.
% 0.96/1.56 { ! hBOOL( hAPP( X, skol15( X ) ) ), hBOOL( hAPP( X,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ) ) }.
% 0.96/1.56 { ! hBOOL( hAPP( X, c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, skol23
% 0.96/1.56 ( X ) ) ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), hBOOL( hAPP( X, Y ) ) }
% 0.96/1.56 .
% 0.96/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ),
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) }.
% 0.96/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) =
% 0.96/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.96/1.56 ( tc_Int_Oint, X, Y ) ) }.
% 0.96/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.96/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 0.96/1.56 ( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.96/1.56 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.96/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 0.96/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) =
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) =
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.56 { c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) }.
% 0.96/1.56 { c_Groups_Oone__class_Oone( tc_Int_Oint ) =
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 0.96/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.96/1.56 { c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 0.96/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone(
% 0.96/1.56 tc_Int_Oint ) }.
% 0.96/1.56 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat( X,
% 0.96/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ) =
% 0.96/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( X, Z ) ), Y ) }.
% 0.96/1.56 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ), hBOOL( hAPP(
% 0.96/1.56 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.56 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.56 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) }.
% 0.96/1.56 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.96/1.56 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) }.
% 0.96/1.56 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ), hBOOL( hAPP(
% 0.96/1.56 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.96/1.56 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.56 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.56 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.96/1.56 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.96/1.56 }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), U ), T ) ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.96/1.56 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 0.96/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.96/1.56 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.96/1.56 ), T ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.96/1.56 ), Z ) = Y }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Odiv( X, Y
% 0.96/1.56 , Z ) ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), c_Divides_Odiv__class_Odiv( X, Y
% 0.96/1.56 , Z ) ) = Y }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.96/1.56 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( X ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.56 c_Power_Opower__class_Opower( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.96/1.56 ), T ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.56 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.56 c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 0.96/1.56 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ), X ) =
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.56 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ), X ) =
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.56 { c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 0.96/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ), X ) }.
% 0.96/1.56 { c_Nat__Transfer_Otsub( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y
% 0.96/1.56 ), c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) =
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.56 { ! class_Rings_Oring__1( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.96/1.56 tc_Nat_Onat, Z, Y ), c_Nat_Osemiring__1__class_Oof__nat( X,
% 0.96/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ) ) =
% 0.96/1.56 c_Groups_Ominus__class_Ominus( X, c_Nat_Osemiring__1__class_Oof__nat( X,
% 0.96/1.56 Y ), c_Nat_Osemiring__1__class_Oof__nat( X, Z ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.96/1.56 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.56 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 0.96/1.56 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.56 tc_Int_Oint, Y, X ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.96/1.56 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Int_Oint ), Y ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.56 tc_Int_Oint, X, Y ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.56 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.96/1.56 , Y ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.96/1.56 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.56 tc_Int_Oint, Y, X ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.56 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.56 tc_Int_Oint, Y, X ) ) }.
% 0.96/1.56 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha10( X, Y ) }.
% 0.96/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.56 { ! alpha10( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.56 { ! alpha10( X, Y ), alpha21( X, Y ), alpha27( X, Y ) }.
% 0.96/1.56 { ! alpha21( X, Y ), alpha10( X, Y ) }.
% 0.96/1.56 { ! alpha27( X, Y ), alpha10( X, Y ) }.
% 0.96/1.56 { ! alpha27( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.56 { ! alpha27( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha27( X, Y ) }.
% 0.96/1.56 { ! alpha21( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.96/1.56 { ! alpha21( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha21( X, Y ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.96/1.56 tc_Int_Oint, X, Y ), X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 0.96/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.96/1.56 tc_Int_Oint, Z, Y ), X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ),
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ),
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.56 { c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, c_Nat_OSuc(
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.96/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ) =
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z ) ), !
% 0.96/1.56 c_Divides_Odiv__class_Odiv( X, Z, Y ) = T, Z = hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z ) ), ! Z =
% 0.96/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( X, Z, Y ) = T }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , Z = c_Groups_Ozero__class_Ozero( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), U ) ), ! c_Divides_Odiv__class_Odiv(
% 0.96/1.56 X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , Z = c_Groups_Ozero__class_Ozero( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), U ) ), ! hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 0.96/1.56 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), c_Nat_Osemiring__1__class_Oof__nat
% 0.96/1.56 ( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.56 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Int_Oint ), c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Nat_Onat ), X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.96/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Z ) ), Y ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Z ) ), X ) ) }.
% 0.96/1.56 { ! hBOOL( hAPP( Z, c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) ), alpha11( X, Y,
% 0.96/1.56 Z ) }.
% 0.96/1.56 { ! hBOOL( hAPP( Z, c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) ), alpha22( X, Y,
% 0.96/1.56 Z ) }.
% 0.96/1.56 { ! alpha11( X, Y, Z ), ! alpha22( X, Y, Z ), hBOOL( hAPP( Z,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) ) }.
% 0.96/1.56 { ! alpha22( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.96/1.56 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.96/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha22( X, Y, Z ) }
% 0.96/1.56 .
% 0.96/1.56 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha22
% 0.96/1.56 ( X, Y, Z ) }.
% 0.96/1.56 { ! alpha11( X, Y, Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.96/1.56 , Y ), hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) ) }.
% 0.96/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), alpha11( X, Y, Z
% 0.96/1.56 ) }.
% 0.96/1.56 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) ), alpha11( X, Y
% 0.96/1.56 , Z ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha12( X, Y, T,
% 0.96/1.56 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha12( X, Y, skol16( X, Y
% 0.96/1.56 , Z ), skol24( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.96/1.56 skol16( X, Y, Z ) ), skol24( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.96/1.56 { ! alpha12( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T
% 0.96/1.56 ) }.
% 0.96/1.56 { ! alpha12( X, Y, Z, T ), alpha23( X, Y, Z, T ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha23( X, Y, Z
% 0.96/1.56 , T ), alpha12( X, Y, Z, T ) }.
% 0.96/1.56 { ! alpha23( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.56 { ! alpha23( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.96/1.56 .
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha23( X,
% 0.96/1.56 Y, Z, T ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv
% 0.96/1.56 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X )
% 0.96/1.56 ) ), ! alpha13( X, Y, T, U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Int_Oint ), X ), alpha13( X, Y, skol17( X, Y, Z ), skol25( X, Y, Z )
% 0.96/1.56 ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X )
% 0.96/1.56 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, skol17( X, Y, Z ) ), skol25
% 0.96/1.56 ( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.96/1.56 tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 0.96/1.56 ) }.
% 0.96/1.56 { ! alpha13( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ) }.
% 0.96/1.56 { ! alpha13( X, Y, Z, T ), alpha24( X, Y, Z, T ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha24( X, Y, Z, T )
% 0.96/1.56 , alpha13( X, Y, Z, T ) }.
% 0.96/1.56 { ! alpha24( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.96/1.56 ) }.
% 0.96/1.56 { ! alpha24( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.96/1.56 .
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha24( X,
% 0.96/1.56 Y, Z, T ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OMin ), X ) =
% 0.96/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.96/1.56 ( tc_Int_Oint ) ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 0.96/1.56 ( X, Z, Y ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.96/1.56 ( X, Y, Z ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.96/1.56 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 0.96/1.56 , Y ) ), Y ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.96/1.56 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.96/1.56 ), Z ), Y ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.96/1.56 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.96/1.56 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.96/1.56 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 T, Z ), Y ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 0.96/1.56 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 T, Y ), Z ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.96/1.56 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.96/1.56 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 0.96/1.56 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 0.96/1.56 ), Z ) }.
% 0.96/1.56 { c_Divides_Odiv__class_Odiv( tc_Int_Oint,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) =
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.56 { c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) =
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ),
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), c_Divides_Odiv__class_Odiv( X
% 0.96/1.56 , c_Groups_Oplus__class_Oplus( X, Y, T ), Z ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Y, Z ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.96/1.56 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 0.96/1.56 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.96/1.56 tc_Nat_Onat, Z, Y ), X ) }.
% 0.96/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), Y ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.56 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.56 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), X =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, c_Nat_OSuc( skol18( X, Y
% 0.96/1.56 ) ) ) ) }.
% 0.96/1.56 { ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, c_Nat_OSuc( Z ) ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), X =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, skol19( X, Y ) ) ) }.
% 0.96/1.56 { ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Z ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.96/1.56 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, c_Nat_Osemiring__1__class_Oof__nat( X, Z
% 0.96/1.56 ), c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) }.
% 0.96/1.56 { ! c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) =
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ), Y = X }.
% 0.96/1.56 { ! Y = X, c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) =
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.96/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 0.96/1.56 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Odiv(
% 0.96/1.56 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.96/1.56 { c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, c_Nat_OSuc( X ) ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.96/1.56 tc_Int_Oint ), c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) }.
% 0.96/1.56 { ! c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) =
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ), Y = X }.
% 0.96/1.56 { ! Y = X, c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) =
% 0.96/1.56 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.96/1.56 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 0.96/1.56 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.96/1.56 ( X ), T, Z ), Y ) }.
% 0.96/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.56 ) ) }.
% 0.96/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 Z, Y ) ) }.
% 0.96/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 Y, Z ) ) }.
% 0.96/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.96/1.56 .
% 0.96/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.96/1.56 .
% 0.96/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.96/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.96/1.56 ) }.
% 0.96/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.96/1.56 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 ) }.
% 0.96/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.96/1.56 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.56 ) }.
% 0.96/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.96/1.56 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.56 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.96/1.56 ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.56 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.96/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.56 ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.96/1.56 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.96/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.56 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.56 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.96/1.56 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.56 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.56 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.96/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.96/1.56 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.96/1.56 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.96/1.56 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.96/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.96/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.96/1.56 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.96/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.96/1.56 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.56 , Y, T ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.96/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.96/1.56 ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.96/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.96/1.56 ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.56 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.96/1.56 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.96/1.56 ) }.
% 0.96/1.56 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.56 T ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), c_Int_Onumber__class_Onumber__of( X, T ) ), Z ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.56 T ) ), Y ) ) }.
% 0.96/1.56 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.56 ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), T ), c_Int_Onumber__class_Onumber__of( X, Y ) ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.96/1.56 ( X, Y ) ) ) }.
% 0.96/1.56 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.96/1.56 W ) ), U ), Y ) }.
% 0.96/1.56 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.56 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), Z ), U ), Y ) }.
% 0.96/1.56 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.96/1.56 Z ) ), U ), T ) = Y }.
% 0.96/1.56 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.96/1.56 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), Z ), U ), Y ) }.
% 0.96/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.96/1.56 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.56 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.96/1.56 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.96/1.56 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.96/1.56 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.96/1.56 Z ) ), Y ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.56 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.56 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.96/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.96/1.56 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.96/1.56 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.96/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.56 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) ) = Y }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ), Y ) = Y }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 0.96/1.56 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.96/1.56 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 0.96/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OPls )
% 0.96/1.56 }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OMin
% 0.96/1.56 ) }.
% 0.96/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OMin ) }
% 0.96/1.56 .
% 0.96/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OPls ) }.
% 0.96/1.56 { ! c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) =
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OMin ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.96/1.56 tc_Int_Oint, X, Y ) ) }.
% 0.96/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.56 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.56 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.96/1.56 .
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.56 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.96/1.56 = X }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.56 tc_Int_Oint ) ) ) }.
% 0.96/1.56 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.56 tc_Int_Oint ) ) ) }.
% 0.96/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Int_OMin ) = c_Int_Opred(
% 0.96/1.56 X ) }.
% 0.96/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OMin, X ) = c_Int_Opred(
% 0.96/1.56 X ) }.
% 0.96/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Int_OPls ) = X }.
% 0.96/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OPls, X ) = X }.
% 0.96/1.56 { ! c_Int_OPls = c_Int_OMin }.
% 0.96/1.56 { ! c_Int_OMin = c_Int_OPls }.
% 0.96/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.96/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.96/1.56 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.96/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.56 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.96/1.56 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.96/1.56 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.96/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 T, Y ), Z = Y }.
% 0.96/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 T, Y ) }.
% 0.96/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 Y, Z ), T = Y }.
% 0.96/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 Y, Z ) }.
% 0.96/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 T, Y ), Z = Y }.
% 0.96/1.56 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 T, Y ), Z = Y }.
% 0.96/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 Y, T ), Z = Y }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X, Y, T
% 0.96/1.56 ) ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.96/1.56 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.96/1.56 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.96/1.56 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.96/1.56 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.96/1.56 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.96/1.56 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.96/1.56 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.96/1.56 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.96/1.56 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.96/1.56 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.96/1.56 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.96/1.56 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.56 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.56 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.56 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.96/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.56 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.96/1.56 ), U = Z, T = Y }.
% 0.96/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.56 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.96/1.56 ) }.
% 0.96/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.56 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.96/1.56 ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.96/1.56 ) ), Z ) }.
% 0.96/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.56 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.56 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.56 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.56 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.96/1.56 ) }.
% 0.96/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.56 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.96/1.56 ), ! U = T }.
% 0.96/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.56 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.96/1.56 ), ! Z = Y }.
% 0.96/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.56 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.96/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.96/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.96/1.56 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.96/1.56 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.56 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.56 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.56 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.96/1.56 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.96/1.56 ) ), T ), Y ) }.
% 0.96/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.96/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.96/1.56 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.96/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Int_Oint ), X ) = X }.
% 0.96/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Int_Oint ) ) = X }.
% 0.96/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.96/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.96/1.56 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 0.96/1.56 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.96/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OMin )
% 0.96/1.56 }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OMin ) }
% 0.96/1.56 .
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.56 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.96/1.56 .
% 0.96/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.96/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.96/1.56 ( X, T, Y ) }.
% 0.96/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.56 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.56 , Y, Z ) ) }.
% 0.96/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.96/1.56 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.56 ( X, Z, Y ) }.
% 0.96/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.56 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.56 , T, Y ) ) }.
% 0.96/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.56 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.56 , Y, T ) ) }.
% 0.96/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.56 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.56 , T, Y ) ) }.
% 0.96/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.56 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.56 , T ) ) }.
% 0.96/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.96/1.56 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.96/1.56 ( X, Z, Y ) }.
% 0.96/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.96/1.56 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.56 ( X, Z, Y ) }.
% 0.96/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.56 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.96/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.56 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.96/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.56 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.56 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.96/1.56 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.96/1.56 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.96/1.56 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.56 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.96/1.56 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.96/1.56 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.96/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.96/1.56 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.56 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.96/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.96/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.56 , c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.96/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, Z ),
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.96/1.56 tc_Int_Oint, Z, Y ) ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X, Z )
% 0.96/1.56 , c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.96/1.56 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Ominus__class_Ominus(
% 0.96/1.56 X, c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.96/1.56 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.96/1.56 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.96/1.56 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ) ), hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), c_Groups_Oplus__class_Oplus
% 0.96/1.56 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ) ) }.
% 0.96/1.56 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.96/1.56 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.56 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.96/1.56 , Z ), X ) ), T ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.56 tc_Int_Oint ), Y ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ) )
% 0.96/1.56 }.
% 0.96/1.56 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ), hBOOL( hAPP
% 0.96/1.56 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.96/1.56 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) )
% 0.96/1.56 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ) }.
% 0.96/1.56 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.56 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.96/1.56 tc_Int_Oint, Z, X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.56 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, X ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.96/1.56 { c_Int_Opred( c_Int_OPls ) = c_Int_OMin }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ),
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 0.96/1.56 ( tc_Int_Oint, X, Y ) = c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.96/1.56 c_Int_OMin ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.96/1.56 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.56 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.96/1.56 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.96/1.56 tc_Nat_Onat, Y, X ), Y ) }.
% 0.96/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.56 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.96/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.56 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.96/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.56 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.96/1.56 ) ) }.
% 0.96/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.56 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.96/1.56 ) ) }.
% 0.96/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.56 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.96/1.56 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.56 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.96/1.56 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.56 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.96/1.56 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.96/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 }.
% 0.96/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 }.
% 0.96/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.96/1.56 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.96/1.56 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.96/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.96/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.96/1.56 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.96/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.96/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.96/1.56 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.96/1.56 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.96/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.56 X, W, Z ) ), U ), T ), Y ) }.
% 0.96/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), Z ), U ), Y ) ) }.
% 0.96/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.96/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.96/1.56 ( X, Z, W ) ), U ), Y ) ) }.
% 0.96/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.96/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.96/1.56 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.96/1.56 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.96/1.56 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.96/1.56 hAPP( Z, skol20( U, W, Z ) ) ) }.
% 0.96/1.56 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.96/1.56 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.96/1.56 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ),
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, skol20( X, Y, Z ),
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ) ) ) ) }.
% 0.96/1.56 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.96/1.56 hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.56 , T, c_Groups_Ozero__class_Ozero( X ) ) ) ), ! hBOOL( hAPP( Z, T ) ),
% 0.96/1.56 hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.96/1.56 skol26( X, Y, Z ) ) ) ) }.
% 0.96/1.56 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.96/1.56 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.96/1.56 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.96/1.56 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.96/1.56 .
% 0.96/1.56 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 0.96/1.56 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X, U, T
% 0.96/1.56 ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ),
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.96/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 0.96/1.56 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 c_Groups_Ominus__class_Ominus( X, U, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ), hBOOL( hAPP(
% 0.96/1.56 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.56 , U, T ) ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 0.96/1.56 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X, U, T
% 0.96/1.56 ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ),
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.96/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 0.96/1.56 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.96/1.56 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 c_Groups_Ominus__class_Ominus( X, U, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ), hBOOL( hAPP(
% 0.96/1.56 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.56 , U, T ) ) ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.96/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.96/1.56 ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.96/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.96/1.56 ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.96/1.56 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.96/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.96/1.56 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 0.96/1.56 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.96/1.56 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.56 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 0.96/1.56 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.96/1.56 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.56 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.96/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Divides_Odiv__class_Odiv
% 0.96/1.56 ( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.96/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Y ) ) =
% 0.96/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Divides_Odiv__class_Omod
% 0.96/1.56 ( tc_Nat_Onat, X, Y ) ) }.
% 0.96/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ), X ) =
% 0.96/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Divides_Odiv__class_Omod
% 0.96/1.56 ( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.56 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat( X,
% 0.96/1.56 c_Nat_OSuc( Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 c_Groups_Oone__class_Oone( X ), c_Nat_Osemiring__1__class_Oof__nat( X, Y
% 0.96/1.56 ) ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 c_Divides_Odiv__class_Omod( X, Z, Y ), hAPP( hAPP(
% 0.96/1.56 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 0.96/1.56 ), Y ) ) = Z }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.96/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), c_Divides_Odiv__class_Omod( X, Y
% 0.96/1.56 , Z ) ) = Y }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.96/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X
% 0.96/1.56 , Z, Y ) ), Y ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), T ), c_Divides_Odiv__class_Odiv( X, Z, T ) ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( X, Z, T ) ), Y ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.96/1.56 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.56 ( X ), c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ),
% 0.96/1.56 c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ) =
% 0.96/1.56 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 0.96/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.96/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), X = c_Groups_Oone__class_Oone(
% 0.96/1.56 tc_Int_Oint ), X = c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.96/1.56 c_Int_OMin ) }.
% 0.96/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) =
% 0.96/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), alpha14( X, Y ), alpha25( X, Y
% 0.96/1.56 ) }.
% 0.96/1.56 { ! alpha14( X, Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint
% 0.96/1.56 ), Y ), X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.56 { ! alpha25( X, Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint
% 0.96/1.56 ), Y ), X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.56 { ! alpha25( X, Y ), Y = c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.96/1.56 c_Int_OMin ) }.
% 0.96/1.56 { ! alpha25( X, Y ), X = c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.96/1.56 c_Int_OMin ) }.
% 0.96/1.56 { ! Y = c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OMin ), ! X =
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OMin ), alpha25( X,
% 0.96/1.56 Y ) }.
% 0.96/1.56 { ! alpha14( X, Y ), Y = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.56 { ! alpha14( X, Y ), X = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.56 { ! Y = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! X =
% 0.96/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), alpha14( X, Y ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.96/1.56 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.56 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X,
% 0.96/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OMin ) ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.96/1.56 tc_Int_Oint ) ), X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.96/1.56 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.96/1.56 }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.96/1.56 tc_Int_Oint ) ), X ) }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.56 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.96/1.56 }.
% 0.96/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.96/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.56 tc_Int_Oint ) ) ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T,
% 0.96/1.56 c_Polynomial_Osmult( X, Y, Z ) ) = c_Polynomial_Osmult( X,
% 0.96/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Divides_Odiv__class_Odiv(
% 0.96/1.56 tc_Polynomial_Opoly( X ), T, Z ) ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.96/1.56 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 0.96/1.56 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.96/1.56 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.96/1.56 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.96/1.56 ) ) }.
% 0.96/1.56 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.96/1.56 .
% 0.96/1.56 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.96/1.56 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.96/1.56 tc_Int_Oint ) }.
% 0.96/1.56 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.56 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.96/1.56 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.56 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.96/1.56 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.96/1.56 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.96/1.56 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.96/1.56 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.96/1.56 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.96/1.56 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.96/1.56 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.96/1.56 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.96/1.56 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.96/1.56 { class_Nat_Osemiring__char__0( tc_Int_Oint ) }.
% 0.96/1.56 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.96/1.56 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.96/1.56 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.96/1.56 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.96/1.56 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Osemiring__1( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.96/1.56 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.96/1.56 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.96/1.56 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.96/1.56 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.96/1.56 { class_Int_Onumber__ring( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.96/1.56 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.96/1.56 { class_Power_Opower( tc_Int_Oint ) }.
% 0.96/1.56 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.96/1.56 { class_Int_Onumber( tc_Int_Oint ) }.
% 0.96/1.56 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.96/1.56 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.96/1.56 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.96/1.56 tc_Nat_Onat ) }.
% 0.96/1.56 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Nat_Osemiring__char__0( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Rings_Osemiring__1( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Int_Onumber( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.96/1.56 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.96/1.56 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.96/1.56 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.96/1.56 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.96/1.56 tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Nat_Osemiring__char__0( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Rings_Osemiring__1( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Int_Onumber__ring( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Int_Onumber( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { ! class_Rings_Oidom( X ),
% 0.96/1.56 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.56 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.96/1.56 ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.56 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.96/1.56 X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.56 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.96/1.56 ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.56 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.56 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.56 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.56 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.96/1.56 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.56 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.56 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.56 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ),
% 0.96/1.56 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.96/1.56 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.96/1.56 ( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.96/1.56 ( tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ), class_Nat_Osemiring__char__0(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Osemiring__1(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 0.96/1.56 ( X ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__ring__1( X ), class_Int_Onumber__ring(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.96/1.56 }.
% 0.96/1.56 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.96/1.56 ) ) }.
% 0.96/1.56 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.96/1.56 .
% 0.96/1.56 { ! class_Rings_Ocomm__ring__1( X ), class_Int_Onumber( tc_Polynomial_Opoly
% 0.96/1.56 ( X ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.96/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.96/1.56 { alpha30, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.96/1.56 ( tc_Complex_Ocomplex ) ), v_p ), hAPP( hAPP(
% 0.96/1.56 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.96/1.56 ), v_q ), c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) ) ) ),
% 0.96/1.56 alpha26 }.
% 0.96/1.56 { alpha30, ! alpha15 }.
% 0.96/1.56 { ! alpha30, alpha15 }.
% 0.96/1.56 { ! alpha30, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.56 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), v_p ), hAPP( hAPP(
% 0.96/1.56 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.96/1.56 ), v_q ), c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) ) ) ) }.
% 0.96/1.56 { ! alpha30, ! alpha26 }.
% 0.96/1.56 { ! alpha15, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.96/1.56 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), v_p ), hAPP( hAPP(
% 0.96/1.56 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.96/1.56 ), v_q ), c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) ) ) ),
% 0.96/1.56 alpha26, alpha30 }.
% 0.96/1.56 { ! alpha26, v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.96/1.56 tc_Complex_Ocomplex ) ) }.
% 0.96/1.56 { ! alpha26, v_q = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.96/1.56 tc_Complex_Ocomplex ) ) }.
% 0.96/1.56 { ! v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.96/1.56 tc_Complex_Ocomplex ) ), ! v_q = c_Groups_Ozero__class_Ozero(
% 0.96/1.56 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), alpha26 }.
% 0.96/1.56 { ! alpha15, ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), X ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.96/1.56 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q ), X ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.96/1.56 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), skol21 ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), alpha15 }.
% 0.96/1.56 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q ), skol21 ) =
% 0.96/1.56 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), alpha15 }.
% 0.96/1.56
% 0.96/1.56 *** allocated 15000 integers for clauses
% 0.96/1.56 *** allocated 22500 integers for clauses
% 0.96/1.56 *** allocated 33750 integers for clauses
% 0.96/1.56 *** allocated 50625 integers for clauses
% 0.96/1.56 *** allocated 75937 integers for clauses
% 0.96/1.56 percentage equality = 0.259889, percentage horn = 0.893544
% 0.96/1.56 This is a problem with some equality
% 0.96/1.56
% 0.96/1.56
% 0.96/1.56
% 0.96/1.56 Options Used:
% 0.96/1.56
% 0.96/1.56 useres = 1
% 0.96/1.56 useparamod = 1
% 0.96/1.56 useeqrefl = 1
% 0.96/1.56 useeqfact = 1
% 0.96/1.56 usefactor = 1
% 0.96/1.56 usesimpsplitting = 0
% 0.96/1.56 usesimpdemod = 5
% 0.96/1.56 usesimpres = 3
% 0.96/1.56
% 0.96/1.56 resimpinuse = 1000
% 0.96/1.56 resimpclauses = 20000
% 0.96/1.56 substype = eqrewr
% 0.96/1.56 backwardsubs = 1
% 0.96/1.56 selectoldest = 5
% 0.96/1.56
% 0.96/1.56 litorderings [0] = split
% 0.96/1.56 litorderings [1] = extend the termordering, first sorting on arguments
% 0.96/1.56
% 0.96/1.56 termordering = kbo
% 0.96/1.56
% 0.96/1.56 litapriori = 0
% 0.96/1.56 termapriori = 1
% 0.96/1.56 litaposteriori = 0
% 0.96/1.56 termaposteriori = 0
% 0.96/1.56 demodaposteriori = 0
% 0.96/1.56 ordereqreflfact = 0
% 0.96/1.56
% 0.96/1.56 litselect = negord
% 0.96/1.56
% 0.96/1.56 maxweight = 15
% 0.96/1.56 maxdepth = 30000
% 0.96/1.56 maxlength = 115
% 0.96/1.56 maxnrvars = 195
% 0.96/1.56 excuselevel = 1
% 0.96/1.56 increasemaxweight = 1
% 0.96/1.56
% 0.96/1.56 maxselected = 10000000
% 0.96/1.56 maxnrclauses = 10000000
% 0.96/1.56
% 0.96/1.56 showgenerated = 0
% 0.96/1.56 showkept = 0
% 0.96/1.56 showselected = 0
% 0.96/1.56 showdeleted = 0
% 0.96/1.56 showresimp = 1
% 0.96/1.56 showstatus = 2000
% 0.96/1.57
% 0.96/1.57 prologoutput = 0
% 0.96/1.57 nrgoals = 5000000
% 0.96/1.57 totalproof = 1
% 0.96/1.57
% 0.96/1.57 Symbols occurring in the translation:
% 0.96/1.57
% 0.96/1.57 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.96/1.57 . [1, 2] (w:1, o:181, a:1, s:1, b:0),
% 0.96/1.57 ! [4, 1] (w:0, o:96, a:1, s:1, b:0),
% 0.96/1.57 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.96/1.57 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.96/1.57 hAPP [38, 2] (w:1, o:205, a:1, s:1, b:0),
% 0.96/1.57 class_Rings_Ocomm__semiring__1 [41, 1] (w:1, o:104, a:1, s:1, b:0),
% 0.96/1.57 c_Rings_Odvd__class_Odvd [42, 1] (w:1, o:105, a:1, s:1, b:0),
% 0.96/1.57 c_Groups_Ozero__class_Ozero [43, 1] (w:1, o:106, a:1, s:1, b:0),
% 0.96/1.57 hBOOL [44, 1] (w:1, o:107, a:1, s:1, b:0),
% 0.96/1.57 tc_Polynomial_Opoly [48, 1] (w:1, o:113, a:1, s:1, b:0),
% 0.96/1.57 c_Power_Opower__class_Opower [49, 1] (w:1, o:114, a:1, s:1, b:0),
% 0.96/1.57 c_Polynomial_Opoly [50, 2] (w:1, o:206, a:1, s:1, b:0),
% 0.96/1.57 class_Rings_Ocomm__semiring__0 [51, 1] (w:1, o:103, a:1, s:1, b:0),
% 0.96/1.57 class_Int_Oring__char__0 [53, 1] (w:1, o:115, a:1, s:1, b:0),
% 0.96/1.57 class_Rings_Oidom [54, 1] (w:1, o:116, a:1, s:1, b:0),
% 0.96/1.57 class_Power_Opower [58, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.96/1.57 class_Rings_Omult__zero [59, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.96/1.57 class_Rings_Ono__zero__divisors [60, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.96/1.57
% 0.96/1.57 class_Rings_Ozero__neq__one [61, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.96/1.57 tc_Nat_Onat [62, 0] (w:1, o:38, a:1, s:1, b:0),
% 0.96/1.57 class_Rings_Oring__1__no__zero__divisors [63, 1] (w:1, o:133, a:1, s:
% 0.96/1.57 1, b:0),
% 0.96/1.57 tc_Complex_Ocomplex [65, 0] (w:1, o:40, a:1, s:1, b:0),
% 0.96/1.57 c_Polynomial_Odegree [66, 2] (w:1, o:208, a:1, s:1, b:0),
% 0.96/1.57 c_Polynomial_Oorder [68, 3] (w:1, o:235, a:1, s:1, b:0),
% 0.96/1.57 class_Groups_Ozero [69, 1] (w:1, o:138, a:1, s:1, b:0),
% 0.96/1.57 c_Polynomial_Osynthetic__div [73, 3] (w:1, o:236, a:1, s:1, b:0),
% 0.96/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [74, 2] (w:1, o:209
% 0.96/1.57 , a:1, s:1, b:0),
% 0.96/1.57 c_Polynomial_Opoly__rec [77, 5] (w:1, o:281, a:1, s:1, b:0),
% 0.96/1.57 c_Orderings_Oord__class_Oless__eq [78, 3] (w:1, o:233, a:1, s:1, b:0)
% 0.96/1.57 ,
% 0.96/1.57 tc_Int_Oint [80, 0] (w:1, o:53, a:1, s:1, b:0),
% 0.96/1.57 class_Fields_Ofield [81, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.96/1.57 c_Polynomial_Osmult [82, 3] (w:1, o:237, a:1, s:1, b:0),
% 0.96/1.57 class_Rings_Olinordered__semidom [84, 1] (w:1, o:125, a:1, s:1, b:0)
% 0.96/1.57 ,
% 0.96/1.57 class_Orderings_Opreorder [86, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.96/1.57 c_Nat_OSuc [87, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.96/1.57 c_Orderings_Oord__class_Oless [88, 3] (w:1, o:234, a:1, s:1, b:0),
% 0.96/1.57 c_Groups_Oone__class_Oone [90, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.96/1.57 c_Groups_Otimes__class_Otimes [91, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.96/1.57 class_Groups_Oab__semigroup__mult [98, 1] (w:1, o:142, a:1, s:1, b:0)
% 0.96/1.57 ,
% 0.96/1.57 class_Groups_Ocomm__monoid__mult [99, 1] (w:1, o:143, a:1, s:1, b:0)
% 0.96/1.57 ,
% 0.96/1.57 class_Groups_Omonoid__mult [100, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.96/1.57 class_Groups_Oone [101, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.96/1.57 class_Orderings_Olinorder [102, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.96/1.57 class_Orderings_Oorder [107, 1] (w:1, o:118, a:1, s:1, b:0),
% 0.96/1.57 class_Orderings_Oord [108, 1] (w:1, o:119, a:1, s:1, b:0),
% 0.96/1.57 class_Rings_Olinordered__idom [111, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.96/1.57 class_Rings_Olinordered__ring [114, 1] (w:1, o:123, a:1, s:1, b:0),
% 0.96/1.57 class_Rings_Olinordered__ring__strict [115, 1] (w:1, o:124, a:1, s:1
% 0.96/1.57 , b:0),
% 0.96/1.57 class_Rings_Olinordered__semiring__strict [116, 1] (w:1, o:127, a:1
% 0.96/1.57 , s:1, b:0),
% 0.96/1.57 class_Rings_Olinordered__comm__semiring__strict [117, 1] (w:1, o:128
% 0.96/1.57 , a:1, s:1, b:0),
% 0.96/1.57 class_Rings_Olinordered__semiring [121, 1] (w:1, o:129, a:1, s:1, b:0
% 0.96/1.57 ),
% 0.96/1.57 class_Rings_Oring__no__zero__divisors [123, 1] (w:1, o:147, a:1, s:1
% 0.96/1.57 , b:0),
% 0.96/1.57 class_Rings_Odvd [124, 1] (w:1, o:149, a:1, s:1, b:0),
% 0.96/1.57 class_Rings_Oordered__cancel__semiring [125, 1] (w:1, o:150, a:1, s:1
% 0.96/1.57 , b:0),
% 0.96/1.57 class_Rings_Oordered__ring [126, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.96/1.57 class_Rings_Oordered__semiring [127, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.96/1.57
% 0.96/1.57 class_Rings_Oordered__comm__semiring [128, 1] (w:1, o:153, a:1, s:1
% 0.96/1.57 , b:0),
% 0.96/1.57 class_Rings_Osemiring__0 [129, 1] (w:1, o:156, a:1, s:1, b:0),
% 0.96/1.57 tc_fun [130, 2] (w:1, o:218, a:1, s:1, b:0),
% 0.96/1.57 c_Power_Opower_Opower [136, 3] (w:1, o:238, a:1, s:1, b:0),
% 0.96/1.57 c_Polynomial_Opcompose [137, 3] (w:1, o:239, a:1, s:1, b:0),
% 0.96/1.57 class_Rings_Ocomm__ring__1 [140, 1] (w:1, o:101, a:1, s:1, b:0),
% 0.96/1.57 c_Polynomial_Omonom [141, 3] (w:1, o:240, a:1, s:1, b:0),
% 0.96/1.57 class_RealVector_Oreal__normed__algebra [142, 1] (w:1, o:157, a:1, s:
% 0.96/1.57 1, b:0),
% 0.96/1.57 c_Polynomial_Ocoeff [149, 2] (w:1, o:207, a:1, s:1, b:0),
% 0.96/1.57 c_Groups_Ominus__class_Ominus [150, 3] (w:1, o:241, a:1, s:1, b:0),
% 0.96/1.57 c_Orderings_Oorder_Omono [151, 4] (w:1, o:267, a:1, s:1, b:0),
% 0.96/1.57 c_Nat__Transfer_Otsub [152, 2] (w:1, o:219, a:1, s:1, b:0),
% 0.96/1.57 class_Groups_Oab__group__add [154, 1] (w:1, o:158, a:1, s:1, b:0),
% 0.96/1.57 class_Rings_Ocomm__ring [156, 1] (w:1, o:102, a:1, s:1, b:0),
% 0.96/1.57 class_Groups_Ogroup__add [161, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.96/1.57 class_Groups_Oordered__ab__group__add [162, 1] (w:1, o:160, a:1, s:1
% 0.96/1.57 , b:0),
% 0.96/1.57 c_Polynomial_Opos__poly [163, 2] (w:1, o:220, a:1, s:1, b:0),
% 0.96/1.57 c_Polynomial_Opoly__gcd [166, 3] (w:1, o:242, a:1, s:1, b:0),
% 0.96/1.57 c_Int_Onumber__class_Onumber__of [168, 2] (w:1, o:221, a:1, s:1, b:0)
% 0.96/1.57 ,
% 0.96/1.57 class_Int_Onumber__ring [169, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.96/1.57 class_Int_Onumber [170, 1] (w:1, o:162, a:1, s:1, b:0),
% 0.96/1.57 class_Rings_Oring [172, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.96/1.57 c_Int_OPls [175, 0] (w:1, o:83, a:1, s:1, b:0),
% 0.96/1.57 c_Rings_Oinverse__class_Oinverse [176, 2] (w:1, o:222, a:1, s:1, b:0)
% 0.96/1.57 ,
% 0.96/1.57 class_Rings_Odivision__ring [177, 1] (w:1, o:163, a:1, s:1, b:0),
% 0.96/1.57 class_Rings_Odivision__ring__inverse__zero [178, 1] (w:1, o:164, a:1
% 0.96/1.57 , s:1, b:0),
% 0.96/1.57 class_Fields_Olinordered__field__inverse__zero [180, 1] (w:1, o:135
% 0.96/1.57 , a:1, s:1, b:0),
% 0.96/1.57 class_Fields_Olinordered__field [181, 1] (w:1, o:136, a:1, s:1, b:0)
% 0.96/1.57 ,
% 0.96/1.57 class_Fields_Ofield__inverse__zero [182, 1] (w:1, o:137, a:1, s:1, b:
% 0.96/1.57 0),
% 0.96/1.57 c_Int_Opred [183, 1] (w:1, o:165, a:1, s:1, b:0),
% 0.96/1.57 c_Divides_Odiv__class_Omod [184, 3] (w:1, o:243, a:1, s:1, b:0),
% 0.96/1.57 class_Divides_Osemiring__div [185, 1] (w:1, o:167, a:1, s:1, b:0),
% 0.96/1.57 class_Divides_Oring__div [188, 1] (w:1, o:166, a:1, s:1, b:0),
% 0.96/1.57 c_Divides_Odiv__class_Odiv [189, 3] (w:1, o:244, a:1, s:1, b:0),
% 0.96/1.57 c_Nat_Osemiring__1__class_Oof__nat [191, 2] (w:1, o:223, a:1, s:1, b:
% 0.96/1.57 0),
% 0.96/1.57 class_Rings_Osemiring__1 [192, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.96/1.57 class_Nat_Osemiring__char__0 [193, 1] (w:1, o:117, a:1, s:1, b:0),
% 0.96/1.57 class_Rings_Oring__1 [194, 1] (w:1, o:155, a:1, s:1, b:0),
% 0.96/1.57 c_Groups_Oplus__class_Oplus [196, 3] (w:1, o:245, a:1, s:1, b:0),
% 0.96/1.57 c_Int_OMin [197, 0] (w:1, o:86, a:1, s:1, b:0),
% 0.96/1.57 class_Groups_Oordered__comm__monoid__add [198, 1] (w:1, o:169, a:1
% 0.96/1.57 , s:1, b:0),
% 0.96/1.57 class_Groups_Olinordered__ab__group__add [199, 1] (w:1, o:144, a:1
% 0.96/1.57 , s:1, b:0),
% 0.96/1.57 class_Groups_Oordered__cancel__ab__semigroup__add [200, 1] (w:1, o:
% 5.87/6.26 170, a:1, s:1, b:0),
% 5.87/6.26 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 5.87/6.26 201, 1] (w:1, o:172, a:1, s:1, b:0),
% 5.87/6.26 class_Rings_Osemiring [202, 1] (w:1, o:171, a:1, s:1, b:0),
% 5.87/6.26 class_Groups_Oab__semigroup__add [206, 1] (w:1, o:173, a:1, s:1, b:0)
% 5.87/6.26 ,
% 5.87/6.26 class_Groups_Ocancel__semigroup__add [207, 1] (w:1, o:174, a:1, s:1
% 5.87/6.26 , b:0),
% 5.87/6.26 class_Groups_Ocancel__ab__semigroup__add [208, 1] (w:1, o:175, a:1
% 5.87/6.26 , s:1, b:0),
% 5.87/6.26 class_Groups_Omonoid__add [209, 1] (w:1, o:176, a:1, s:1, b:0),
% 5.87/6.26 class_Groups_Ocomm__monoid__add [210, 1] (w:1, o:177, a:1, s:1, b:0)
% 5.87/6.26 ,
% 5.87/6.26 class_Rings_Ocomm__semiring [211, 1] (w:1, o:148, a:1, s:1, b:0),
% 5.87/6.26 class_Groups_Oordered__ab__semigroup__add__imp__le [213, 1] (w:1, o:
% 5.87/6.26 178, a:1, s:1, b:0),
% 5.87/6.26 class_Groups_Oordered__ab__semigroup__add [214, 1] (w:1, o:179, a:1
% 5.87/6.26 , s:1, b:0),
% 5.87/6.26 class_Groups_Ocancel__comm__monoid__add [217, 1] (w:1, o:180, a:1, s:
% 5.87/6.26 1, b:0),
% 5.87/6.26 tc_HOL_Obool [219, 0] (w:1, o:52, a:1, s:1, b:0),
% 5.87/6.26 v_p [220, 0] (w:1, o:91, a:1, s:1, b:0),
% 5.87/6.26 v_q [221, 0] (w:1, o:92, a:1, s:1, b:0),
% 5.87/6.26 alpha1 [222, 3] (w:1, o:246, a:1, s:1, b:1),
% 5.87/6.26 alpha2 [223, 2] (w:1, o:226, a:1, s:1, b:1),
% 5.87/6.26 alpha3 [224, 4] (w:1, o:270, a:1, s:1, b:1),
% 5.87/6.26 alpha4 [225, 4] (w:1, o:274, a:1, s:1, b:1),
% 5.87/6.26 alpha5 [226, 3] (w:1, o:247, a:1, s:1, b:1),
% 5.87/6.26 alpha6 [227, 3] (w:1, o:248, a:1, s:1, b:1),
% 5.87/6.26 alpha7 [228, 2] (w:1, o:227, a:1, s:1, b:1),
% 5.87/6.26 alpha8 [229, 2] (w:1, o:228, a:1, s:1, b:1),
% 5.87/6.26 alpha9 [230, 2] (w:1, o:229, a:1, s:1, b:1),
% 5.87/6.26 alpha10 [231, 2] (w:1, o:224, a:1, s:1, b:1),
% 5.87/6.26 alpha11 [232, 3] (w:1, o:249, a:1, s:1, b:1),
% 5.87/6.26 alpha12 [233, 4] (w:1, o:275, a:1, s:1, b:1),
% 5.87/6.26 alpha13 [234, 4] (w:1, o:276, a:1, s:1, b:1),
% 5.87/6.26 alpha14 [235, 2] (w:1, o:225, a:1, s:1, b:1),
% 5.87/6.26 alpha15 [236, 0] (w:1, o:93, a:1, s:1, b:1),
% 5.87/6.26 alpha16 [237, 4] (w:1, o:277, a:1, s:1, b:1),
% 5.87/6.26 alpha17 [238, 4] (w:1, o:278, a:1, s:1, b:1),
% 5.87/6.26 alpha18 [239, 4] (w:1, o:279, a:1, s:1, b:1),
% 5.87/6.26 alpha19 [240, 3] (w:1, o:250, a:1, s:1, b:1),
% 5.87/6.26 alpha20 [241, 3] (w:1, o:251, a:1, s:1, b:1),
% 5.87/6.26 alpha21 [242, 2] (w:1, o:230, a:1, s:1, b:1),
% 5.87/6.26 alpha22 [243, 3] (w:1, o:252, a:1, s:1, b:1),
% 5.87/6.26 alpha23 [244, 4] (w:1, o:268, a:1, s:1, b:1),
% 5.87/6.26 alpha24 [245, 4] (w:1, o:269, a:1, s:1, b:1),
% 5.87/6.26 alpha25 [246, 2] (w:1, o:231, a:1, s:1, b:1),
% 5.87/6.26 alpha26 [247, 0] (w:1, o:94, a:1, s:1, b:1),
% 5.87/6.26 alpha27 [248, 2] (w:1, o:232, a:1, s:1, b:1),
% 5.87/6.26 alpha28 [249, 3] (w:1, o:253, a:1, s:1, b:1),
% 5.87/6.26 alpha29 [250, 3] (w:1, o:254, a:1, s:1, b:1),
% 5.87/6.26 alpha30 [251, 0] (w:1, o:95, a:1, s:1, b:1),
% 5.87/6.26 alpha31 [252, 3] (w:1, o:255, a:1, s:1, b:1),
% 5.87/6.26 alpha32 [253, 4] (w:1, o:271, a:1, s:1, b:1),
% 5.87/6.26 alpha33 [254, 4] (w:1, o:272, a:1, s:1, b:1),
% 5.87/6.26 alpha34 [255, 4] (w:1, o:273, a:1, s:1, b:1),
% 5.87/6.26 skol1 [256, 2] (w:1, o:210, a:1, s:1, b:1),
% 5.87/6.26 skol2 [257, 2] (w:1, o:215, a:1, s:1, b:1),
% 5.87/6.26 skol3 [258, 2] (w:1, o:216, a:1, s:1, b:1),
% 5.87/6.26 skol4 [259, 1] (w:1, o:108, a:1, s:1, b:1),
% 5.87/6.26 skol5 [260, 3] (w:1, o:256, a:1, s:1, b:1),
% 5.87/6.26 skol6 [261, 3] (w:1, o:257, a:1, s:1, b:1),
% 5.87/6.26 skol7 [262, 3] (w:1, o:258, a:1, s:1, b:1),
% 5.87/6.26 skol8 [263, 3] (w:1, o:259, a:1, s:1, b:1),
% 5.87/6.26 skol9 [264, 2] (w:1, o:217, a:1, s:1, b:1),
% 5.87/6.26 skol10 [265, 4] (w:1, o:280, a:1, s:1, b:1),
% 5.87/6.26 skol11 [266, 2] (w:1, o:211, a:1, s:1, b:1),
% 5.87/6.26 skol12 [267, 2] (w:1, o:212, a:1, s:1, b:1),
% 5.87/6.26 skol13 [268, 3] (w:1, o:260, a:1, s:1, b:1),
% 5.87/6.26 skol14 [269, 1] (w:1, o:109, a:1, s:1, b:1),
% 5.87/6.26 skol15 [270, 1] (w:1, o:110, a:1, s:1, b:1),
% 5.87/6.26 skol16 [271, 3] (w:1, o:261, a:1, s:1, b:1),
% 5.87/6.26 skol17 [272, 3] (w:1, o:262, a:1, s:1, b:1),
% 5.87/6.26 skol18 [273, 2] (w:1, o:213, a:1, s:1, b:1),
% 5.87/6.26 skol19 [274, 2] (w:1, o:214, a:1, s:1, b:1),
% 5.87/6.26 skol20 [275, 3] (w:1, o:263, a:1, s:1, b:1),
% 5.87/6.26 skol21 [276, 0] (w:1, o:37, a:1, s:1, b:1),
% 5.87/6.26 skol22 [277, 1] (w:1, o:111, a:1, s:1, b:1),
% 5.87/6.26 skol23 [278, 1] (w:1, o:112, a:1, s:1, b:1),
% 39.17/39.52 skol24 [279, 3] (w:1, o:264, a:1, s:1, b:1),
% 39.17/39.52 skol25 [280, 3] (w:1, o:265, a:1, s:1, b:1),
% 39.17/39.52 skol26 [281, 3] (w:1, o:266, a:1, s:1, b:1).
% 39.17/39.52
% 39.17/39.52
% 39.17/39.52 Starting Search:
% 39.17/39.52
% 39.17/39.52 *** allocated 113905 integers for clauses
% 39.17/39.52 *** allocated 170857 integers for clauses
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52
% 39.17/39.52 Intermediate Status:
% 39.17/39.52 Generated: 3531
% 39.17/39.52 Kept: 2097
% 39.17/39.52 Inuse: 53
% 39.17/39.52 Deleted: 3
% 39.17/39.52 Deletedinuse: 0
% 39.17/39.52
% 39.17/39.52 *** allocated 170857 integers for termspace/termends
% 39.17/39.52 *** allocated 256285 integers for clauses
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52
% 39.17/39.52 Intermediate Status:
% 39.17/39.52 Generated: 8391
% 39.17/39.52 Kept: 4103
% 39.17/39.52 Inuse: 129
% 39.17/39.52 Deleted: 3
% 39.17/39.52 Deletedinuse: 0
% 39.17/39.52
% 39.17/39.52 *** allocated 256285 integers for termspace/termends
% 39.17/39.52 *** allocated 384427 integers for clauses
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52
% 39.17/39.52 Intermediate Status:
% 39.17/39.52 Generated: 12072
% 39.17/39.52 Kept: 6155
% 39.17/39.52 Inuse: 162
% 39.17/39.52 Deleted: 4
% 39.17/39.52 Deletedinuse: 0
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52 *** allocated 384427 integers for termspace/termends
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52 *** allocated 576640 integers for clauses
% 39.17/39.52
% 39.17/39.52 Intermediate Status:
% 39.17/39.52 Generated: 15485
% 39.17/39.52 Kept: 8192
% 39.17/39.52 Inuse: 203
% 39.17/39.52 Deleted: 7
% 39.17/39.52 Deletedinuse: 0
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52
% 39.17/39.52 Intermediate Status:
% 39.17/39.52 Generated: 19216
% 39.17/39.52 Kept: 10212
% 39.17/39.52 Inuse: 239
% 39.17/39.52 Deleted: 8
% 39.17/39.52 Deletedinuse: 0
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52 *** allocated 576640 integers for termspace/termends
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52 *** allocated 864960 integers for clauses
% 39.17/39.52
% 39.17/39.52 Intermediate Status:
% 39.17/39.52 Generated: 26570
% 39.17/39.52 Kept: 12218
% 39.17/39.52 Inuse: 270
% 39.17/39.52 Deleted: 8
% 39.17/39.52 Deletedinuse: 0
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52
% 39.17/39.52 Intermediate Status:
% 39.17/39.52 Generated: 31207
% 39.17/39.52 Kept: 14345
% 39.17/39.52 Inuse: 288
% 39.17/39.52 Deleted: 8
% 39.17/39.52 Deletedinuse: 0
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52
% 39.17/39.52 Intermediate Status:
% 39.17/39.52 Generated: 36193
% 39.17/39.52 Kept: 16356
% 39.17/39.52 Inuse: 316
% 39.17/39.52 Deleted: 9
% 39.17/39.52 Deletedinuse: 0
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52 *** allocated 864960 integers for termspace/termends
% 39.17/39.52 *** allocated 1297440 integers for clauses
% 39.17/39.52
% 39.17/39.52 Intermediate Status:
% 39.17/39.52 Generated: 43669
% 39.17/39.52 Kept: 18789
% 39.17/39.52 Inuse: 336
% 39.17/39.52 Deleted: 10
% 39.17/39.52 Deletedinuse: 0
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52 Resimplifying clauses:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52
% 39.17/39.52 Intermediate Status:
% 39.17/39.52 Generated: 50024
% 39.17/39.52 Kept: 20822
% 39.17/39.52 Inuse: 363
% 39.17/39.52 Deleted: 237
% 39.17/39.52 Deletedinuse: 0
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52
% 39.17/39.52 Intermediate Status:
% 39.17/39.52 Generated: 55243
% 39.17/39.52 Kept: 22824
% 39.17/39.52 Inuse: 399
% 39.17/39.52 Deleted: 237
% 39.17/39.52 Deletedinuse: 0
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52
% 39.17/39.52 Intermediate Status:
% 39.17/39.52 Generated: 58683
% 39.17/39.52 Kept: 24827
% 39.17/39.52 Inuse: 406
% 39.17/39.52 Deleted: 237
% 39.17/39.52 Deletedinuse: 0
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52
% 39.17/39.52 Intermediate Status:
% 39.17/39.52 Generated: 64427
% 39.17/39.52 Kept: 27435
% 39.17/39.52 Inuse: 441
% 39.17/39.52 Deleted: 237
% 39.17/39.52 Deletedinuse: 0
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52 *** allocated 1946160 integers for clauses
% 39.17/39.52 *** allocated 1297440 integers for termspace/termends
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52
% 39.17/39.52 Intermediate Status:
% 39.17/39.52 Generated: 71073
% 39.17/39.52 Kept: 29673
% 39.17/39.52 Inuse: 471
% 39.17/39.52 Deleted: 237
% 39.17/39.52 Deletedinuse: 0
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52
% 39.17/39.52 Intermediate Status:
% 39.17/39.52 Generated: 77392
% 39.17/39.52 Kept: 31690
% 39.17/39.52 Inuse: 499
% 39.17/39.52 Deleted: 239
% 39.17/39.52 Deletedinuse: 2
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52
% 39.17/39.52 Intermediate Status:
% 39.17/39.52 Generated: 81447
% 39.17/39.52 Kept: 34330
% 39.17/39.52 Inuse: 506
% 39.17/39.52 Deleted: 239
% 39.17/39.52 Deletedinuse: 2
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52
% 39.17/39.52 Intermediate Status:
% 39.17/39.52 Generated: 87990
% 39.17/39.52 Kept: 37710
% 39.17/39.52 Inuse: 526
% 39.17/39.52 Deleted: 240
% 39.17/39.52 Deletedinuse: 3
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52
% 39.17/39.52 Intermediate Status:
% 39.17/39.52 Generated: 94008
% 39.17/39.52 Kept: 39726
% 39.17/39.52 Inuse: 543
% 39.17/39.52 Deleted: 240
% 39.17/39.52 Deletedinuse: 3
% 39.17/39.52
% 39.17/39.52 Resimplifying clauses:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52
% 39.17/39.52 Intermediate Status:
% 39.17/39.52 Generated: 101338
% 39.17/39.52 Kept: 41741
% 39.17/39.52 Inuse: 564
% 39.17/39.52 Deleted: 437
% 39.17/39.52 Deletedinuse: 3
% 39.17/39.52
% 39.17/39.52 Resimplifying inuse:
% 39.17/39.52 Done
% 39.17/39.52
% 39.17/39.52 *** allocated 2919240 integers for clauses
% 39.17/39.52
% 39.17/39.52 Intermediate Status:
% 39.17/39.52 Generated: 106265
% 39.17/39.52 Kept: 43914
% 39.17/39.52 Inuse: 581
% 39.17/39.52 Deleted: 437
% 115.72/116.13 Deletedinuse: 3
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 114220
% 115.72/116.13 Kept: 45955
% 115.72/116.13 Inuse: 621
% 115.72/116.13 Deleted: 437
% 115.72/116.13 Deletedinuse: 3
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13 *** allocated 1946160 integers for termspace/termends
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 120879
% 115.72/116.13 Kept: 49656
% 115.72/116.13 Inuse: 636
% 115.72/116.13 Deleted: 437
% 115.72/116.13 Deletedinuse: 3
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 135612
% 115.72/116.13 Kept: 52995
% 115.72/116.13 Inuse: 666
% 115.72/116.13 Deleted: 437
% 115.72/116.13 Deletedinuse: 3
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 147817
% 115.72/116.13 Kept: 56158
% 115.72/116.13 Inuse: 686
% 115.72/116.13 Deleted: 437
% 115.72/116.13 Deletedinuse: 3
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 154554
% 115.72/116.13 Kept: 58240
% 115.72/116.13 Inuse: 706
% 115.72/116.13 Deleted: 437
% 115.72/116.13 Deletedinuse: 3
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 158836
% 115.72/116.13 Kept: 60287
% 115.72/116.13 Inuse: 714
% 115.72/116.13 Deleted: 437
% 115.72/116.13 Deletedinuse: 3
% 115.72/116.13
% 115.72/116.13 Resimplifying clauses:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 166620
% 115.72/116.13 Kept: 62378
% 115.72/116.13 Inuse: 729
% 115.72/116.13 Deleted: 569
% 115.72/116.13 Deletedinuse: 3
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 174127
% 115.72/116.13 Kept: 64389
% 115.72/116.13 Inuse: 768
% 115.72/116.13 Deleted: 573
% 115.72/116.13 Deletedinuse: 7
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 182365
% 115.72/116.13 Kept: 66890
% 115.72/116.13 Inuse: 780
% 115.72/116.13 Deleted: 574
% 115.72/116.13 Deletedinuse: 7
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13 *** allocated 4378860 integers for clauses
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 187765
% 115.72/116.13 Kept: 68900
% 115.72/116.13 Inuse: 823
% 115.72/116.13 Deleted: 574
% 115.72/116.13 Deletedinuse: 7
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 193713
% 115.72/116.13 Kept: 71056
% 115.72/116.13 Inuse: 875
% 115.72/116.13 Deleted: 574
% 115.72/116.13 Deletedinuse: 7
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 201702
% 115.72/116.13 Kept: 73303
% 115.72/116.13 Inuse: 905
% 115.72/116.13 Deleted: 574
% 115.72/116.13 Deletedinuse: 7
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13 *** allocated 2919240 integers for termspace/termends
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 208636
% 115.72/116.13 Kept: 75357
% 115.72/116.13 Inuse: 930
% 115.72/116.13 Deleted: 574
% 115.72/116.13 Deletedinuse: 7
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 213995
% 115.72/116.13 Kept: 77679
% 115.72/116.13 Inuse: 942
% 115.72/116.13 Deleted: 574
% 115.72/116.13 Deletedinuse: 7
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 225566
% 115.72/116.13 Kept: 80518
% 115.72/116.13 Inuse: 970
% 115.72/116.13 Deleted: 574
% 115.72/116.13 Deletedinuse: 7
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13 Resimplifying clauses:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 235508
% 115.72/116.13 Kept: 84953
% 115.72/116.13 Inuse: 995
% 115.72/116.13 Deleted: 2646
% 115.72/116.13 Deletedinuse: 7
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 243994
% 115.72/116.13 Kept: 89096
% 115.72/116.13 Inuse: 1020
% 115.72/116.13 Deleted: 2646
% 115.72/116.13 Deletedinuse: 7
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 250329
% 115.72/116.13 Kept: 91605
% 115.72/116.13 Inuse: 1060
% 115.72/116.13 Deleted: 2646
% 115.72/116.13 Deletedinuse: 7
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 268443
% 115.72/116.13 Kept: 95093
% 115.72/116.13 Inuse: 1080
% 115.72/116.13 Deleted: 2646
% 115.72/116.13 Deletedinuse: 7
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 290829
% 115.72/116.13 Kept: 98043
% 115.72/116.13 Inuse: 1095
% 115.72/116.13 Deleted: 2646
% 115.72/116.13 Deletedinuse: 7
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 313252
% 115.72/116.13 Kept: 100718
% 115.72/116.13 Inuse: 1105
% 115.72/116.13 Deleted: 2646
% 115.72/116.13 Deletedinuse: 7
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13 Resimplifying clauses:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 319521
% 115.72/116.13 Kept: 103595
% 115.72/116.13 Inuse: 1115
% 115.72/116.13 Deleted: 2925
% 115.72/116.13 Deletedinuse: 7
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13 *** allocated 6568290 integers for clauses
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 325337
% 115.72/116.13 Kept: 106249
% 115.72/116.13 Inuse: 1133
% 115.72/116.13 Deleted: 2927
% 115.72/116.13 Deletedinuse: 9
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13 Resimplifying inuse:
% 115.72/116.13 Done
% 115.72/116.13
% 115.72/116.13
% 115.72/116.13 Intermediate Status:
% 115.72/116.13 Generated: 329505
% 115.72/116.13 KCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------