TSTP Solution File: SWW271+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW271+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 23:21:44 EDT 2022
% Result : Timeout 300.06s 300.52s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW271+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Mon Jun 6 08:54:18 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.32/1.72 *** allocated 10000 integers for termspace/termends
% 1.32/1.72 *** allocated 10000 integers for clauses
% 1.32/1.72 *** allocated 10000 integers for justifications
% 1.32/1.72 *** allocated 15000 integers for termspace/termends
% 1.32/1.72 *** allocated 22500 integers for termspace/termends
% 1.32/1.72 *** allocated 33750 integers for termspace/termends
% 1.32/1.72 Bliksem 1.12
% 1.32/1.72
% 1.32/1.72
% 1.32/1.72 Automatic Strategy Selection
% 1.32/1.72
% 1.32/1.72 *** allocated 50625 integers for termspace/termends
% 1.32/1.72 *** allocated 75937 integers for termspace/termends
% 1.32/1.72 *** allocated 113905 integers for termspace/termends
% 1.32/1.72
% 1.32/1.72 Clauses:
% 1.32/1.72
% 1.32/1.72 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.32/1.72 { ! v_qa____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.32/1.72 tc_Complex_Ocomplex ) ) }.
% 1.32/1.72 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.32/1.72 tc_Complex_Ocomplex ) ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, v_a____ ),
% 1.32/1.72 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 1.32/1.72 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.32/1.72 tc_Complex_Ocomplex ) ) ) ) ), v_qa____ ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 1.32/1.72 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ) ) }.
% 1.32/1.72 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.72 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.72 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.32/1.72 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 1.32/1.72 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 1.32/1.72 ) }.
% 1.32/1.72 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 1.32/1.72 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 1.32/1.72 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.32/1.72 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.72 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.32/1.72 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 1.32/1.72 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 1.32/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.72 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.32/1.72 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.32/1.72 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.32/1.72 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.32/1.72 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.32/1.72 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.32/1.72 { ! v_pa____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.32/1.72 tc_Complex_Ocomplex ) ) }.
% 1.32/1.72 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.32/1.72 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.32/1.72 ( X, Y ) ) }.
% 1.32/1.72 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.32/1.72 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.32/1.72 ) ), Y ) }.
% 1.32/1.72 { ! v_na____ = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.72 { ! c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) )
% 1.32/1.72 }.
% 1.32/1.72 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_a____ ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.32/1.72 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 1.32/1.72 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_qa____ ), X ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), Y ), Y ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) )
% 1.32/1.72 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.72 ( X ), T ), Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 1.32/1.72 ), Z ), Y ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.72 ( X ), Z ), T ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 1.32/1.72 ), Z ), Y ) ) }.
% 1.32/1.72 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.72 ( X ), Y ), T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z
% 1.32/1.72 ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), U ), T ) ), hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.72 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T
% 1.32/1.72 ) ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), c_Groups_Oone__class_Oone( X ) ), Y ) ) }
% 1.32/1.72 .
% 1.32/1.72 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ouminus__class_Ouminus( X, Z ) )
% 1.32/1.72 , Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ouminus__class_Ouminus( X, Z ) )
% 1.32/1.72 , Y ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ouminus__class_Ouminus( X, Y
% 1.32/1.72 ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ouminus__class_Ouminus( X, Y
% 1.32/1.72 ) ) ) }.
% 1.32/1.72 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.32/1.72 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.72 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.72 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 1.32/1.72 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), T =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 1.32/1.72 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 1.32/1.72 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.32/1.72 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.72 X ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 1.32/1.72 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.32/1.72 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.72 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 1.32/1.72 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), Z =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), T ), Y ) ) }.
% 1.32/1.72 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 1.32/1.72 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.32/1.72 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.72 X ), T ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 1.32/1.72 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.32/1.72 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.32/1.72 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 1.32/1.72 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.32/1.72 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 1.32/1.72 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 1.32/1.72 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 1.32/1.72 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.72 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.72 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.72 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.32/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.72 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.32/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.72 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.32/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.32/1.72 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.32/1.72 = Y }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.32/1.72 = Y }.
% 1.32/1.72 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.32/1.72 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.32/1.72 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.32/1.72 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.32/1.72 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.32/1.72 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.32/1.72 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.32/1.72 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.32/1.72 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.32/1.72 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.32/1.72 ( X, Y ) ) }.
% 1.32/1.72 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.32/1.72 tc_Complex_Ocomplex ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.32/1.72 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 1.32/1.72 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 1.32/1.72 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 1.32/1.72 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 1.32/1.72 ) ) ), c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____, v_pa____ ) ) )
% 1.32/1.72 , v_pa____ ) ) }.
% 1.32/1.72 { ! v_qa____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.32/1.72 tc_Complex_Ocomplex ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.72 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), v_pa____ ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 1.32/1.72 ), v_qa____ ), v_na____ ) ) ) }.
% 1.32/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.32/1.72 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.32/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.32/1.72 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.32/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.32/1.72 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.32/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.32/1.72 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.32/1.72 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.32/1.72 = Y }.
% 1.32/1.72 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.32/1.72 = Y }.
% 1.32/1.72 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.32/1.72 = Y }.
% 1.32/1.72 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.32/1.72 = Y }.
% 1.32/1.72 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.32/1.72 = Y }.
% 1.32/1.72 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.32/1.72 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.32/1.72 ) }.
% 1.32/1.72 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.32/1.72 ) }.
% 1.32/1.72 { ! v_n = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.72 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), X ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 1.32/1.72 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q ), X ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.32/1.72 { c_Polynomial_Odegree( tc_Complex_Ocomplex, v_pa____ ) = v_na____ }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.32/1.72 tc_Nat_Onat ) ) = Y }.
% 1.32/1.72 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.32/1.72 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 1.32/1.72 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 1.32/1.72 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.32/1.72 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.32/1.72 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 1.32/1.72 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.32/1.72 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.32/1.72 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.72 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.32/1.72 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.32/1.72 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.72 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 1.32/1.72 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.32/1.72 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.32/1.72 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.32/1.72 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.32/1.72 ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.32/1.72 ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.32/1.72 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.32/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.32/1.72 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.32/1.72 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.32/1.72 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.32/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.32/1.72 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.32/1.72 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.32/1.72 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.32/1.72 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.32/1.72 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 1.32/1.72 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.32/1.72 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.32/1.72 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.32/1.72 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 1.32/1.72 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.32/1.72 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 1.32/1.72 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.32/1.72 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 1.32/1.72 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 1.32/1.72 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.32/1.72 { ! class_Rings_Oidom( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.32/1.72 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Oorder( X, Z, Y ) ) ), Y )
% 1.32/1.72 ) }.
% 1.32/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.32/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.32/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.32/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.32/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons
% 1.32/1.72 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 1.32/1.72 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ) }.
% 1.32/1.72 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 1.32/1.72 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ), hAPP( c_Polynomial_Opoly( X, Z )
% 1.32/1.72 , Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X, Z,
% 1.32/1.72 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ),
% 1.32/1.72 hAPP( c_Polynomial_Opoly( X, Y ), c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.32/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.32/1.72 X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 1.32/1.72 ) ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.32/1.72 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) }.
% 1.32/1.72 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 1.32/1.72 = Y }.
% 1.32/1.72 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 1.32/1.72 ) }.
% 1.32/1.72 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 1.32/1.72 ( X ) }.
% 1.32/1.72 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 1.32/1.72 , Y ) }.
% 1.32/1.72 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.32/1.72 tc_Complex_Ocomplex ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.32/1.72 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 1.32/1.72 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 1.32/1.72 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 1.32/1.72 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 1.32/1.72 ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( tc_Complex_Ocomplex, v_a____,
% 1.32/1.72 v_pa____ ) ) ) ), v_pa____ ) ) }.
% 1.32/1.72 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Oorder(
% 1.32/1.72 tc_Complex_Ocomplex, X, v_pa____ ), v_na____ ) }.
% 1.32/1.72 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.32/1.72 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.32/1.72 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.32/1.72 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.32/1.72 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.32/1.72 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.32/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.32/1.72 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.32/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.32/1.72 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.32/1.72 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.32/1.72 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.32/1.72 .
% 1.32/1.72 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.32/1.72 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.32/1.72 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Nat_Onat ) }.
% 1.32/1.72 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.32/1.72 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.32/1.72 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.32/1.72 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.32/1.72 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.32/1.72 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.32/1.72 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.32/1.72 Y ) ) ) ), Y ) ) }.
% 1.32/1.72 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.32/1.72 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Oorder( X, Z, Y ) ) ), Y )
% 1.32/1.72 ) }.
% 1.32/1.72 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.32/1.72 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.32/1.72 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.32/1.72 Y ) ) ) ), Y ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.32/1.72 X ), Z ), T ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T )
% 1.32/1.72 ) ) }.
% 1.32/1.72 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.32/1.72 = c_Groups_Oone__class_Oone( X ) }.
% 1.32/1.72 { c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) = v_n }.
% 1.32/1.72 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.32/1.72 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.32/1.72 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.32/1.72 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.32/1.72 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.32/1.72 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 1.32/1.72 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.32/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 1.32/1.72 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 1.32/1.72 , c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Z, Y ) ), c_Nat_OSuc(
% 1.32/1.72 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), c_Orderings_Oord__class_Oless__eq
% 1.32/1.72 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 1.32/1.72 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.72 c_Polynomial_Odegree( X, Z ) ), Y ) ) }.
% 1.32/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.32/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.32/1.72 X ), Y ), Z = Y }.
% 1.32/1.72 { ! class_Rings_Olinordered__semidom( X ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.72 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.32/1.72 { ! class_Rings_Olinordered__semidom( X ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 1.32/1.72 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.32/1.72 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.32/1.72 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 1.32/1.72 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ), Z ), Y ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 1.32/1.72 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.32/1.72 }.
% 1.32/1.72 { ! class_Rings_Olinordered__semidom( X ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.32/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 1.32/1.72 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.32/1.72 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 1.32/1.72 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 1.32/1.72 ) }.
% 1.32/1.72 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.32/1.72 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.32/1.72 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.32/1.72 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.32/1.72 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.32/1.72 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.32/1.72 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.32/1.72 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 1.32/1.72 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.32/1.72 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.32/1.72 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 1.32/1.72 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.32/1.72 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.32/1.72 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.32/1.72 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 1.32/1.72 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.32/1.72 c_Polynomial_Odegree( X, Y ) }.
% 1.32/1.72 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.32/1.72 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.72 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.32/1.72 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.32/1.72 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.32/1.72 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.32/1.72 { ! class_Rings_Olinordered__semidom( X ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.32/1.72 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.32/1.72 { ! class_Rings_Olinordered__semidom( X ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.72 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.32/1.72 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.32/1.72 { ! class_Rings_Olinordered__semidom( X ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.32/1.72 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.32/1.72 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.32/1.72 X ), T ), Z ) ), Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 1.32/1.72 , U, Z ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 1.32/1.72 c_Power_Opower__class_Opower( X ), T ), U ) ), Y ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.72 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ), hBOOL( hAPP( hAPP
% 1.32/1.72 ( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 1.32/1.72 ( X ), Z ), U ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T
% 1.32/1.72 ) ) ) }.
% 1.32/1.72 { ! class_Rings_Ocomm__semiring__1( X ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP
% 1.32/1.72 ( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 1.32/1.72 ( X ), T ), Z ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y
% 1.32/1.72 ) ) ) }.
% 1.32/1.72 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.32/1.72 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.72 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.32/1.72 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.32/1.72 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 1.32/1.72 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.32/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.72 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.32/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.32/1.72 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.32/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.72 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.32/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.32/1.72 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.32/1.72 ( X ) ) }.
% 1.32/1.72 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.32/1.72 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.72 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.32/1.72 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.32/1.72 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.32/1.72 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.32/1.72 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.32/1.72 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.32/1.72 { ! class_Rings_Oordered__semiring( X ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.32/1.72 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.32/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.32/1.72 { ! class_Rings_Oordered__semiring( X ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.32/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.32/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.32/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.32/1.73 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.32/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.32/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.32/1.73 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.32/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.32/1.73 { ! class_Rings_Oordered__comm__semiring( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.32/1.73 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.32/1.73 { ! class_Rings_Oordered__semiring( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.32/1.73 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.32/1.73 { ! class_Rings_Oordered__semiring( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.32/1.73 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.32/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.32/1.73 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.32/1.73 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.32/1.73 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( X ) ) }.
% 1.32/1.73 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.32/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.73 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.32/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.73 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( X ) ), alpha1( X, Y, Z ), alpha19( X, Y, Z ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( X ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha19( X, Y, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( X ) ) }.
% 1.32/1.73 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.73 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.32/1.73 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( X ), Y ), alpha19( X, Y, Z ) }.
% 1.32/1.73 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.32/1.73 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ), alpha1( X, Y, Z ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha2( X, Y
% 1.32/1.73 , Z ), alpha20( X, Y, Z ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha20( X, Y, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.32/1.73 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.73 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.32/1.73 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ), alpha20( X, Y, Z ) }.
% 1.32/1.73 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.32/1.73 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), Y ), alpha2( X, Y, Z ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.32/1.73 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.73 c_Groups_Oone__class_Oone( X ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.32/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.32/1.73 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.32/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.32/1.73 ( X, Y ), Y ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.32/1.73 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.73 ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.32/1.73 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.32/1.73 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.32/1.73 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 1.32/1.73 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.32/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.32/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.32/1.73 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.32/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.32/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.32/1.73 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 1.32/1.73 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.32/1.73 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.32/1.73 tc_Nat_Onat ) ) = Y }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 1.32/1.73 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 1.32/1.73 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.32/1.73 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 1.32/1.73 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( X ) }.
% 1.32/1.73 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.32/1.73 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.32/1.73 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 1.32/1.73 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, v_na____ ), ! hAPP(
% 1.32/1.73 c_Polynomial_Opoly( tc_Complex_Ocomplex, Z ), skol2( T, Z ) ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 1.32/1.73 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = X, X =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), Y
% 1.32/1.73 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 1.32/1.73 tc_Complex_Ocomplex ) ), Z ), X ) ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, v_na____ ), hAPP(
% 1.32/1.73 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), skol2( Y, Z ) ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 1.32/1.73 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = X, X =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), Y
% 1.32/1.73 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 1.32/1.73 tc_Complex_Ocomplex ) ), Z ), X ) ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.32/1.73 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.32/1.73 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.32/1.73 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 1.32/1.73 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.32/1.73 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.32/1.73 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.32/1.73 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 1.32/1.73 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 1.32/1.73 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.32/1.73 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.32/1.73 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.32/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.32/1.73 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.32/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.32/1.73 ), X ) ) }.
% 1.32/1.73 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.32/1.73 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), X ) ) }
% 1.32/1.73 .
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.32/1.73 X ) ) }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 1.32/1.73 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.32/1.73 , X ) ) }.
% 1.32/1.73 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X )
% 1.32/1.73 , Y ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.32/1.73 ), Y = X }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , alpha3( X, Y ), Y = X }.
% 1.32/1.73 { ! alpha3( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.73 tc_Nat_Onat ), Y ), X ) ) }.
% 1.32/1.73 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.32/1.73 , X ) ) }.
% 1.32/1.73 { ! alpha3( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.73 tc_Nat_Onat ), Y ), X ) ) }.
% 1.32/1.73 { ! alpha3( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.73 tc_Nat_Onat ), X ), Y ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.32/1.73 , alpha3( X, Y ) }.
% 1.32/1.73 { ! alpha4( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.73 tc_Nat_Onat ), Y ), X ) ) }.
% 1.32/1.73 { ! alpha4( X, Y ), ! Y = X }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , Y = X, alpha4( X, Y ) }.
% 1.32/1.73 { ! alpha4( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.73 tc_Nat_Onat ), Y ), X ) ) }.
% 1.32/1.73 { ! alpha4( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.73 tc_Nat_Onat ), X ), Y ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.32/1.73 , alpha4( X, Y ) }.
% 1.32/1.73 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.32/1.73 , X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.32/1.73 , X ) ) }.
% 1.32/1.73 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.32/1.73 , X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.32/1.73 ), Y ) ) }.
% 1.32/1.73 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.32/1.73 , X ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.32/1.73 ), X = Y }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , ! X = Y, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.32/1.73 ), Y ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , Y = X }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.32/1.73 ), Y = X }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.32/1.73 , X ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.32/1.73 ), Y ) ) }.
% 1.32/1.73 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.32/1.73 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 1.32/1.73 ), Z ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 1.32/1.73 ), Z ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.32/1.73 ), Y = X }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.32/1.73 ), Y = X }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.32/1.73 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.32/1.73 ) }.
% 1.32/1.73 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.32/1.73 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 1.32/1.73 ), X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 1.32/1.73 ), Z ) ) }.
% 1.32/1.73 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.32/1.73 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 1.32/1.73 ), X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 1.32/1.73 Z ), Y ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.32/1.73 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 1.32/1.73 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.32/1.73 ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.32/1.73 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 1.32/1.73 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 1.32/1.73 ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.32/1.73 , ! Y = X }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.32/1.73 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.32/1.73 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 1.32/1.73 ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.32/1.73 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.32/1.73 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 1.32/1.73 ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.32/1.73 , ! Y = X }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.32/1.73 , ! X = Y }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.32/1.73 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 1.32/1.73 ), Z ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.32/1.73 , ! X = Z, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 1.32/1.73 Z ), Y ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.32/1.73 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.32/1.73 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.32/1.73 ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.32/1.73 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.32/1.73 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 1.32/1.73 ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.32/1.73 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.32/1.73 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 1.32/1.73 ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.32/1.73 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.32/1.73 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 1.32/1.73 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.32/1.73 ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.32/1.73 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.32/1.73 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 1.32/1.73 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 1.32/1.73 ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.32/1.73 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.32/1.73 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 1.32/1.73 ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.32/1.73 X, Y, Z ) }.
% 1.32/1.73 { alpha47( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.32/1.73 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.32/1.73 { alpha47( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.32/1.73 ( X, Y ), Z ) ) }.
% 1.32/1.73 { ! alpha47( X, Y, Z ), alpha50( X, Y, Z ), Z = Y }.
% 1.32/1.73 { ! alpha47( X, Y, Z ), alpha50( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.32/1.73 ) ) }.
% 1.32/1.73 { ! alpha50( X, Y, Z ), alpha47( X, Y, Z ) }.
% 1.32/1.73 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha47( X, Y, Z ) }.
% 1.32/1.73 { ! alpha50( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 1.32/1.73 }.
% 1.32/1.73 { ! alpha50( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 1.32/1.73 X, Y ), Z ) ), alpha50( X, Y, Z ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.32/1.73 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.32/1.73 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.32/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ), X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.32/1.73 .
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 1.32/1.73 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X
% 1.32/1.73 ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ), X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.32/1.73 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 1.32/1.73 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 1.32/1.73 .
% 1.32/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 1.32/1.73 .
% 1.32/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.32/1.73 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.32/1.73 X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.32/1.73 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 1.32/1.73 }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.32/1.73 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.32/1.73 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.32/1.73 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.32/1.73 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 1.32/1.73 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 1.32/1.73 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.32/1.73 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.32/1.73 ( X, Y ), Z ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.32/1.73 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.32/1.73 ( X, Z ), Y ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.32/1.73 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 1.32/1.73 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.32/1.73 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 1.32/1.73 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.32/1.73 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.32/1.73 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.32/1.73 ), X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha5( X, Y ) }.
% 1.32/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.32/1.73 { ! alpha5( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.32/1.73 c_Nat_OSuc( X ) ) }.
% 1.32/1.73 { ! alpha5( X, Y ), Y = c_Nat_OSuc( skol3( Z, Y ) ) }.
% 1.32/1.73 { ! alpha5( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol3( X, Y
% 1.32/1.73 ), X ) }.
% 1.32/1.73 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.32/1.73 ), alpha5( X, Y ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol4( X ) ) }.
% 1.32/1.73 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 1.32/1.73 .
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.32/1.73 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.32/1.73 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.73 Y ), X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ), Z ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.32/1.73 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ), Y ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.32/1.73 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.32/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.32/1.73 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.32/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.32/1.73 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.32/1.73 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ), Z ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.73 tc_Nat_Onat ), Y ), X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.32/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.32/1.73 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.32/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.32/1.73 ), X ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.32/1.73 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.32/1.73 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.32/1.73 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 1.32/1.73 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.32/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha6( X, Y, Z, T ),
% 1.32/1.73 alpha21( X, Y, Z, T ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z, T ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha21( X, Y, Z, T ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.32/1.73 { ! alpha21( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.73 { ! alpha21( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.32/1.73 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha21( X, Y, Z, T ) }.
% 1.32/1.73 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.32/1.73 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.32/1.73 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha6( X, Y, Z, T ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha7( X, Y, Z, T ),
% 1.32/1.73 alpha22( X, Y, Z, T ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha7( X, Y, Z, T ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha22( X, Y, Z, T ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.32/1.73 { ! alpha22( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.73 { ! alpha22( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.32/1.73 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha22( X, Y, Z, T ) }.
% 1.32/1.73 { ! alpha7( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.32/1.73 { ! alpha7( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.32/1.73 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha7( X, Y, Z, T ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.32/1.73 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.32/1.73 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.32/1.73 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.32/1.73 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.32/1.73 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.32/1.73 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.32/1.73 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( X ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.32/1.73 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.32/1.73 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( X ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.32/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.32/1.73 .
% 1.32/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.32/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.32/1.73 .
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.32/1.73 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.32/1.73 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.32/1.73 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.32/1.73 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.32/1.73 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( X ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.32/1.73 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.32/1.73 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.32/1.73 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.32/1.73 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.32/1.73 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.32/1.73 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.32/1.73 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.32/1.73 .
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.32/1.73 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.32/1.73 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.32/1.73 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.32/1.73 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 , Y ) }.
% 1.32/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.32/1.73 , Y ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.32/1.73 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.32/1.73 .
% 1.32/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.32/1.73 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.32/1.73 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.32/1.73 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 1.32/1.73 ) }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.32/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.32/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.32/1.73 ) }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.32/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.32/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.73 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.73 X ), Y ) ), X ) ), Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.32/1.73 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.73 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.73 Y ), X ) ), X ) ), Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.32/1.73 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ), X ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.32/1.73 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ) ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.32/1.73 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.32/1.73 ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.32/1.73 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.32/1.73 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.32/1.73 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.32/1.73 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.32/1.73 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.32/1.73 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.32/1.73 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.32/1.73 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.32/1.73 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.32/1.73 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.32/1.73 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.32/1.73 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.32/1.73 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.32/1.73 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 1.32/1.73 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.73 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.32/1.73 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.32/1.73 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.32/1.73 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 1.32/1.73 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.32/1.73 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.32/1.73 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 1.32/1.73 { ! c_Nat_OSuc( X ) = X }.
% 1.32/1.73 { ! X = c_Nat_OSuc( X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 1.32/1.73 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 1.32/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.32/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.32/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.32/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X =
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.32/1.73 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone(
% 1.32/1.73 tc_Nat_Onat ) ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 1.32/1.73 c_Groups_Oone__class_Oone( X ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.32/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 1.32/1.73 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), hBOOL( hAPP
% 1.32/1.73 ( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 1.32/1.73 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.32/1.73 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.32/1.73 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.32/1.73 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 1.32/1.73 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.32/1.73 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.32/1.73 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hBOOL(
% 1.32/1.73 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.32/1.73 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.32/1.73 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.32/1.73 ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.32/1.73 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 1.32/1.73 }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.32/1.73 c_Nat_OSuc( X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.32/1.73 ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.32/1.73 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.32/1.73 , c_Nat_OSuc( X ) ) }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 1.32/1.73 .
% 1.32/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.32/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.32/1.73 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.32/1.73 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.32/1.73 .
% 1.32/1.73 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.32/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.32/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.32/1.73 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.32/1.73 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.32/1.73 .
% 1.32/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.32/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.32/1.73 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.73 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 1.32/1.73 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.73 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.32/1.73 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.32/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.32/1.73 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.32/1.73 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.32/1.73 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.32/1.73 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.32/1.73 , Y ), X ) }.
% 1.32/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.32/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.32/1.73 tc_Nat_Onat ) }.
% 1.32/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.32/1.73 tc_Nat_Onat ) }.
% 1.32/1.73 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.32/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.32/1.73 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 1.32/1.73 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.32/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.32/1.73 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 1.32/1.73 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.32/1.73 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.32/1.73 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 1.32/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 1.32/1.73 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.73 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.73 X ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 1.32/1.73 , Y ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 1.32/1.73 ), Y ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.73 tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.73 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.73 X ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 1.32/1.73 , Y ) ) ) }.
% 1.32/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.32/1.73 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.32/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.32/1.73 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ), Y =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.32/1.73 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ), Y ) }.
% 1.32/1.73 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.32/1.73 ), X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.32/1.73 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), Z =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 1.32/1.73 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.32/1.73 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.32/1.73 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.32/1.73 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.73 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.32/1.73 tc_Nat_Onat ), X ), Y ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.32/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.32/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.32/1.73 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 1.32/1.73 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ), Y =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ) }.
% 1.32/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ), hBOOL( hAPP(
% 1.32/1.73 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.32/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ) }.
% 1.32/1.73 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.32/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.32/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.32/1.73 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.32/1.73 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.32/1.73 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.32/1.73 .
% 1.32/1.73 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.73 tc_Nat_Onat ), Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ),
% 1.32/1.73 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ),
% 1.32/1.73 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 1.32/1.73 c_Polynomial_Odegree( X, Y ) ) }.
% 1.32/1.73 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 1.32/1.73 , Y ) }.
% 1.32/1.73 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.32/1.73 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.32/1.73 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Opcompose( X, Z, Y )
% 1.32/1.73 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.73 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.32/1.73 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 1.32/1.73 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.32/1.73 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.32/1.73 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.32/1.73 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 1.32/1.73 ) ) }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.32/1.73 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.32/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.32/1.73 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.32/1.73 hAPP( Y, U ) ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.32/1.73 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.32/1.73 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.32/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.32/1.73 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.32/1.73 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.32/1.73 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.32/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 1.32/1.73 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.32/1.73 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.32/1.73 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.32/1.73 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.32/1.73 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.32/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.32/1.73 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.32/1.73 hAPP( Y, U ) ) }.
% 1.32/1.73 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.32/1.73 ( X, Z, Y ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.32/1.73 ( X, Y, Z ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.32/1.73 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.32/1.73 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.32/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.32/1.73 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.32/1.73 hAPP( Y, U ) ) }.
% 1.32/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 1.32/1.73 ( Z, skol5( X, Y, Z ) ), hAPP( Y, skol5( X, Y, Z ) ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.32/1.73 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.32/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.32/1.73 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.32/1.73 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.32/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.32/1.73 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.32/1.73 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.32/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.32/1.73 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 1.32/1.73 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.32/1.73 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 1.32/1.73 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.32/1.73 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.32/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.32/1.73 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.32/1.73 , ! Y = Z }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.32/1.73 , ! Z = Y }.
% 1.32/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.32/1.73 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.32/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.32/1.73 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.32/1.73 , ! Z = Y }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.32/1.73 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.32/1.73 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.32/1.73 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.32/1.73 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.32/1.73 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.32/1.73 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.32/1.73 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.32/1.73 Y ), ! Z = Y }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.32/1.73 Z ), ! Z = Y }.
% 1.32/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.32/1.73 Y ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), !
% 1.32/1.73 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ),
% 1.32/1.73 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.32/1.73 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.32/1.73 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.32/1.73 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.32/1.73 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.32/1.73 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.32/1.73 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.32/1.73 , ! Z = Y }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.32/1.73 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.32/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.32/1.73 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.32/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.32/1.73 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.32/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.32/1.73 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.32/1.73 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.32/1.73 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.32/1.73 ( X, Z, Y ) }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.32/1.73 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.32/1.73 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.32/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.32/1.73 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.32/1.73 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.32/1.73 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.32/1.73 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.32/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.32/1.73 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.32/1.73 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.32/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.32/1.73 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.32/1.73 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.32/1.73 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.32/1.73 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.32/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.32/1.73 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.32/1.73 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.32/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.32/1.73 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.32/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.32/1.73 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.32/1.73 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.32/1.73 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.32/1.73 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ), alpha8
% 1.32/1.73 ( X, Y, Z ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.32/1.73 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__idom( X ), ! alpha8( X, Y, Z ),
% 1.32/1.73 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.32/1.73 { ! alpha8( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 1.32/1.73 ( X ) ) }.
% 1.32/1.73 { ! alpha8( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.32/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.32/1.73 alpha8( X, Y, Z ) }.
% 1.32/1.73 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.32/1.73 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.32/1.73 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.32/1.73 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.32/1.73 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.32/1.73 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.32/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.32/1.73 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 1.32/1.73 .
% 1.32/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.32/1.73 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 1.32/1.73 }.
% 1.32/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.32/1.73 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 1.32/1.73 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.32/1.73 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.32/1.73 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 1.32/1.73 .
% 1.32/1.73 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.32/1.73 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.32/1.73 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.32/1.73 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 1.32/1.73 ( X, Y ), Z = Y }.
% 1.32/1.73 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 1.32/1.73 ( X, Y ) }.
% 1.32/1.73 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.32/1.73 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 1.32/1.73 ) ) }.
% 1.32/1.73 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 1.32/1.73 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), ! hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP( hAPP
% 1.32/1.73 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ), X = Y }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 1.32/1.73 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), Z =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.32/1.73 , ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 1.32/1.73 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X
% 1.32/1.73 ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.32/1.73 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 1.32/1.73 tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 1.32/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.32/1.73 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 1.32/1.73 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 1.32/1.73 X, Z ), Y ) ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 1.32/1.73 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 1.32/1.73 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 1.32/1.73 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.32/1.73 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.32/1.73 }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 1.32/1.73 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.32/1.73 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), ! hAPP(
% 1.32/1.73 c_Polynomial_Ocoeff( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 1.32/1.73 , Y ) }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 1.32/1.73 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.32/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.32/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.32/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.32/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.32/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.32/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.32/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.32/1.73 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.32/1.73 ( tc_Int_Oint ) }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.32/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.32/1.73 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.32/1.73 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.32/1.73 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.32/1.73 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Int_Oint ), X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.32/1.73 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.32/1.73 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 1.32/1.73 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol6( X
% 1.32/1.73 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol6( X, Y, Z ) ), Z = Y
% 1.32/1.73 }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 1.32/1.73 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 1.32/1.73 c_Polynomial_Ocoeff( X, Y ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 1.32/1.73 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 1.32/1.73 c_Polynomial_Omonom( X, Y, Z ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.32/1.73 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ) ) = Z }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.32/1.73 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 1.32/1.73 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.73 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 1.32/1.73 ) ) }.
% 1.32/1.73 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.32/1.73 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.32/1.73 c_Polynomial_Odegree( X, Y ) ), ! hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), ! hBOOL
% 1.32/1.73 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Y ),
% 1.32/1.73 Z ) ), Z = Y }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.73 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.73 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 1.32/1.73 , c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Z, Y ) ), Y ) }.
% 1.32/1.73 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.32/1.73 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.32/1.73 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.32/1.73 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 1.32/1.73 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 1.32/1.73 tc_Nat_Onat, Y, c_Polynomial_Odegree( X, Z ) ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.32/1.73 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.32/1.73 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.32/1.73 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 1.32/1.73 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.73 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.32/1.73 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 1.32/1.73 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.32/1.73 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 1.32/1.73 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 1.32/1.73 ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 1.32/1.73 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 1.32/1.73 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.32/1.73 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.32/1.73 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.32/1.73 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.32/1.73 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 1.32/1.73 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.32/1.73 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 1.32/1.73 ( X ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 1.32/1.73 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 1.32/1.73 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 1.32/1.73 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 1.32/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 1.32/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ), hBOOL( hAPP(
% 1.32/1.73 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.32/1.73 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 1.32/1.73 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 1.32/1.73 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 1.32/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.32/1.73 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.32/1.73 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.32/1.73 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.32/1.73 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.32/1.73 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.32/1.73 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.32/1.73 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.32/1.73 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.32/1.73 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.32/1.73 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.32/1.73 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.32/1.73 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 1.32/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.32/1.73 ) ) }.
% 1.32/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.32/1.73 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.32/1.73 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.32/1.73 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.32/1.73 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.32/1.73 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.32/1.73 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.32/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.32/1.73 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 1.32/1.73 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.32/1.73 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.32/1.73 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, Z, Y ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 1.32/1.73 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, Z, Y ) }.
% 1.32/1.73 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 1.32/1.73 , T ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.32/1.73 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.32/1.73 , T, Y ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.32/1.73 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 1.32/1.73 , Y, T ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.32/1.73 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, Z, Y ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.32/1.73 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.32/1.73 , T, Y ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.32/1.73 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, T, Y ) }.
% 1.32/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.32/1.73 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.32/1.73 , Y, Z ) ) }.
% 1.32/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.32/1.73 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.73 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.32/1.73 ), U = Z, T = Y }.
% 1.32/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.32/1.73 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.73 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.32/1.73 ) }.
% 1.32/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.32/1.73 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.73 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.32/1.73 ) }.
% 1.32/1.73 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 1.32/1.73 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.73 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 1.32/1.73 ) ), T ), Y ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 1.32/1.73 ) ), Z ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.32/1.73 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.32/1.73 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.32/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.32/1.73 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.73 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.32/1.73 ) }.
% 1.32/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.32/1.73 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.73 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.32/1.73 ), ! U = T }.
% 1.32/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.32/1.73 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.73 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.32/1.73 ), ! Z = Y }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.32/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.32/1.73 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.32/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.32/1.73 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.32/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.32/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.32/1.73 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 Z, Y ) ) = Y }.
% 1.32/1.73 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.32/1.73 Y ) ) = Y }.
% 1.32/1.73 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.32/1.73 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.32/1.73 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.32/1.73 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.32/1.73 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 1.32/1.73 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 1.32/1.73 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.32/1.73 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X, Y, T
% 1.32/1.73 ) ) ) }.
% 1.32/1.73 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 Y, T ), Z = Y }.
% 1.32/1.73 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 T, Y ), Z = Y }.
% 1.32/1.73 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 T, Y ), Z = Y }.
% 1.32/1.73 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 Y, Z ), T = Y }.
% 1.32/1.73 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 Y, Z ) }.
% 1.32/1.73 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 T, Y ), Z = Y }.
% 1.32/1.73 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 T, Y ) }.
% 1.32/1.73 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.32/1.73 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.32/1.73 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 1.32/1.73 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.32/1.73 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.32/1.73 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.32/1.73 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.32/1.73 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.32/1.73 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.32/1.73 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.32/1.73 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.32/1.73 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.32/1.73 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.32/1.73 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.32/1.73 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.32/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.73 ) }.
% 1.32/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.32/1.73 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.32/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 1.32/1.73 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 ) }.
% 1.32/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 1.32/1.73 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.32/1.73 ) }.
% 1.32/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.32/1.73 .
% 1.32/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.32/1.73 .
% 1.32/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.32/1.73 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 Y, Z ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 Z, Y ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.32/1.73 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 1.32/1.73 ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.32/1.73 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.32/1.73 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 1.32/1.73 ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.32/1.73 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.32/1.73 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.32/1.73 ) ) }.
% 1.32/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 1.32/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.32/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.32/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.32/1.73 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 1.32/1.73 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.32/1.73 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.32/1.73 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.32/1.73 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.32/1.73 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.32/1.73 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.32/1.73 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.32/1.73 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.32/1.73 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.32/1.73 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.32/1.73 hAPP( Z, skol7( U, W, Z ) ) ) }.
% 1.32/1.73 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.32/1.73 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.32/1.73 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, skol7( X, Y, Z ),
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ) ) ) }.
% 1.32/1.73 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.32/1.73 hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Oplus__class_Oplus( X
% 1.32/1.73 , T, c_Groups_Ozero__class_Ozero( X ) ) ) ), ! hBOOL( hAPP( Z, T ) ),
% 1.32/1.73 hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 1.32/1.73 skol27( X, Y, Z ) ) ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 1.32/1.73 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.32/1.73 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 1.32/1.73 , Y, T ) ) }.
% 1.32/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.32/1.73 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.73 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.32/1.73 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 1.32/1.73 ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.73 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.32/1.73 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.32/1.73 ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.32/1.73 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.32/1.73 ) }.
% 1.32/1.73 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.32/1.73 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.32/1.73 Z ) = Y }.
% 1.32/1.73 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.73 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.73 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.32/1.73 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.73 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.32/1.73 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 1.32/1.73 ( X, Y ) }.
% 1.32/1.73 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 X ) }.
% 1.32/1.73 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.32/1.73 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 1.32/1.73 ( X, Z ) }.
% 1.32/1.73 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.32/1.73 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 1.32/1.73 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 1.32/1.73 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.32/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 1.32/1.73 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.32/1.73 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.32/1.73 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.32/1.73 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.32/1.73 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.32/1.73 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.32/1.73 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.32/1.73 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 1.32/1.73 .
% 1.32/1.73 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.32/1.73 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.32/1.73 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.32/1.73 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.32/1.73 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.32/1.73 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.32/1.73 { ! class_Groups_Ocomm__monoid__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.32/1.73 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.73 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 1.32/1.73 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 1.32/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.32/1.73 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.73 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.32/1.73 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.32/1.73 ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.32/1.73 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.32/1.73 ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.32/1.73 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.32/1.73 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.32/1.73 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.32/1.73 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.32/1.73 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.32/1.73 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.32/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.73 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.32/1.73 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.32/1.73 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.32/1.73 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.32/1.73 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.32/1.73 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.32/1.73 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 1.32/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 1.32/1.73 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ), hBOOL( hAPP( hAPP
% 1.32/1.73 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) ), hBOOL( hAPP(
% 1.32/1.73 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semiring__1( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.32/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 1.32/1.73 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.73 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 1.32/1.73 ), Y ) }.
% 1.32/1.73 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.32/1.73 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( X ), U ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 1.32/1.73 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 1.32/1.73 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 1.32/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.32/1.73 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.32/1.73 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Int_Oint ) ) }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.32/1.73 tc_Int_Oint ) ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.32/1.73 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 1.32/1.73 }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.32/1.73 , alpha33( X, Y, Z, T ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha33( X, Y, Z, T ),
% 1.32/1.73 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 1.32/1.73 { ! alpha33( X, Y, Z, T ), alpha9( X, Z, T ) }.
% 1.32/1.73 { ! alpha33( X, Y, Z, T ), alpha23( X, Y, T ) }.
% 1.32/1.73 { ! alpha9( X, Z, T ), ! alpha23( X, Y, T ), alpha33( X, Y, Z, T ) }.
% 1.32/1.73 { ! alpha23( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ), alpha34( X, Y, Z ) }.
% 1.32/1.73 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha23( X
% 1.32/1.73 , Y, Z ) }.
% 1.32/1.73 { ! alpha34( X, Y, Z ), alpha23( X, Y, Z ) }.
% 1.32/1.73 { ! alpha34( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.32/1.73 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 1.32/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha34( X
% 1.32/1.73 , Y, Z ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 1.32/1.73 ), c_Polynomial_Odegree( X, Z ) ), alpha34( X, Y, Z ) }.
% 1.32/1.73 { ! alpha9( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.73 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha9( X, Y
% 1.32/1.73 , Z ) }.
% 1.32/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha9( X
% 1.32/1.73 , Y, Z ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.32/1.73 , skol8( T, U, Z ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.73 c_Polynomial_Odegree( X, Y ), Z ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ), skol8( X
% 1.32/1.73 , Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.32/1.73 Y ), Z ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.32/1.73 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.32/1.73 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.73 }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.32/1.73 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.32/1.73 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 1.32/1.73 .
% 1.32/1.73 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.32/1.73 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.32/1.73 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 1.32/1.73 .
% 1.32/1.73 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.32/1.73 Z, c_Polynomial_Odegree( X, Y ) ), c_Orderings_Oord__class_Oless(
% 1.32/1.73 tc_Nat_Onat, Z, skol9( T, U, Z ) ) }.
% 1.32/1.73 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.32/1.73 Z, c_Polynomial_Odegree( X, Y ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.32/1.73 skol9( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) ), Y ) ) }
% 1.32/1.73 .
% 1.32/1.73 { ! class_Fields_Ofield( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) ), Z ) ) }
% 1.32/1.73 .
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol10( X, Y ) ) }.
% 1.32/1.73 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.32/1.73 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Int_Oint ), X ) = X }.
% 1.32/1.73 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Int_Oint ) ) = X }.
% 1.32/1.73 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.32/1.73 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.32/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.32/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.32/1.73 .
% 1.32/1.73 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ) ) = X }.
% 1.32/1.73 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ), X ) = X }.
% 1.32/1.73 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 1.32/1.73 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 1.32/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.32/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.32/1.73 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.32/1.73 ( tc_Nat_Onat, Y, X ), X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.32/1.73 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 1.32/1.73 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 1.32/1.73 .
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.32/1.73 .
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.32/1.73 .
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.32/1.73 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.32/1.73 , X ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ), hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.32/1.73 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.32/1.73 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.32/1.73 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.32/1.73 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.32/1.73 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.32/1.73 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 1.32/1.73 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 1.32/1.73 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.32/1.73 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 1.32/1.73 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 1.32/1.73 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.32/1.73 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.32/1.73 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.32/1.73 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 1.32/1.73 .
% 1.32/1.73 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.32/1.73 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), T ) ), hBOOL(
% 1.32/1.73 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ),
% 1.32/1.73 c_Polynomial_Opoly__gcd( X, Y, T ) ) ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.32/1.73 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Opoly__gcd( X, Z, Y ) ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 1.32/1.73 , T ), Z ) ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.32/1.73 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Opoly__gcd( X, Z, Y ) ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 1.32/1.73 , T ), Y ) ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.32/1.73 ( tc_Polynomial_Opoly( X ) ), T ), Z ) ), ! hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Y ) ), hBOOL(
% 1.32/1.73 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 1.32/1.73 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 1.32/1.73 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z,
% 1.32/1.73 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.32/1.73 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Nat_Onat, Z, Y ) ) }.
% 1.32/1.73 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.32/1.73 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.32/1.73 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha10( X, Y ), alpha24( X
% 1.32/1.73 , Y ) }.
% 1.32/1.73 { ! alpha10( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.32/1.73 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.32/1.73 { ! alpha24( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.32/1.73 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.32/1.73 { ! alpha24( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! alpha24( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ) ) }.
% 1.32/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha24( X, Y ) }.
% 1.32/1.73 { ! alpha10( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ) ) }.
% 1.32/1.73 { ! alpha10( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha10( X, Y ) }.
% 1.32/1.73 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha11( X, Y ),
% 1.32/1.73 alpha25( X, Y ) }.
% 1.32/1.73 { ! alpha11( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.32/1.73 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! alpha25( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.32/1.73 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! alpha25( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! alpha25( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ) ) }.
% 1.32/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha25( X, Y ) }.
% 1.32/1.73 { ! alpha11( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ) ) }.
% 1.32/1.73 { ! alpha11( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.73 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha11( X, Y ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.32/1.73 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Nat_Onat, Y, X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.73 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Nat_Onat, Y, X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Int_Oint, X, Y ) ) }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.32/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol11( X, Y ) ) ) }.
% 1.32/1.73 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.32/1.73 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.32/1.73 .
% 1.32/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 1.32/1.73 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.32/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 1.32/1.73 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.32/1.73 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 1.32/1.73 = X }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.32/1.73 tc_Int_Oint ) ) ) }.
% 1.32/1.73 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.32/1.73 tc_Int_Oint ) ) ) }.
% 1.32/1.73 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 1.32/1.73 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.32/1.73 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.32/1.73 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.32/1.73 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ) ), hBOOL( hAPP( hAPP(
% 1.32/1.73 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), c_Groups_Oplus__class_Oplus
% 1.32/1.73 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.32/1.73 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.32/1.73 , Z ), X ) ), T ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.73 tc_Int_Oint ), Y ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ) )
% 1.32/1.73 }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ), hBOOL( hAPP
% 1.32/1.73 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.32/1.73 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) )
% 1.32/1.73 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ) }.
% 1.32/1.73 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 1.32/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.32/1.73 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.32/1.73 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.32/1.73 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.32/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.32/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.32/1.73 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 1.32/1.73 }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.32/1.73 tc_Int_Oint ) ) ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.32/1.73 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 1.32/1.73 }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.32/1.73 tc_Int_Oint ) ), X ) }.
% 1.32/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.32/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.32/1.73 tc_Int_Oint ) ), X ) }.
% 1.32/1.73 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.32/1.73 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 1.32/1.73 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 1.32/1.74 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 1.32/1.74 ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.32/1.74 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ),
% 1.32/1.74 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.32/1.74 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 1.32/1.74 c_Polynomial_Odegree( X, Z ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.32/1.74 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.32/1.74 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 1.32/1.74 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.32/1.74 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.32/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.32/1.74 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.32/1.74 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.32/1.74 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.32/1.74 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.32/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.32/1.74 ( tc_Int_Oint ), Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.32/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.32/1.74 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.32/1.74 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.32/1.74 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.32/1.74 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 1.32/1.74 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 1.32/1.74 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.32/1.74 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 1.32/1.74 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 1.32/1.74 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.32/1.74 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 1.32/1.74 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.32/1.74 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.32/1.74 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.32/1.74 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 1.32/1.74 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.32/1.74 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.32/1.74 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.32/1.74 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.32/1.74 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 1.32/1.74 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.32/1.74 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.32/1.74 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 1.32/1.74 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.32/1.74 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), alpha51( X, Y, Z, T ), ! Y =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.32/1.74 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 1.32/1.74 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.32/1.74 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), alpha51( X, Y, Z, T ), ! hAPP(
% 1.32/1.74 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 1.32/1.74 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 1.32/1.74 .
% 1.32/1.74 { ! alpha51( X, Y, Z, T ), alpha52( X, Y, Z, T ), alpha48( X, Y, T ) }.
% 1.32/1.74 { ! alpha51( X, Y, Z, T ), alpha52( X, Y, Z, T ), ! hAPP(
% 1.32/1.74 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.74 { ! alpha52( X, Y, Z, T ), alpha51( X, Y, Z, T ) }.
% 1.32/1.74 { ! alpha48( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.32/1.74 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.74 alpha51( X, Y, Z, T ) }.
% 1.32/1.74 { ! alpha52( X, Y, Z, T ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ), Z ), T ) ), alpha53( X, Y, Z, T ) }.
% 1.32/1.74 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ),
% 1.32/1.74 Z ), T ) ), alpha52( X, Y, Z, T ) }.
% 1.32/1.74 { ! alpha53( X, Y, Z, T ), alpha52( X, Y, Z, T ) }.
% 1.32/1.74 { ! alpha53( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ), skol12( X, Y, U, W ) ), Y ) ) }.
% 1.32/1.74 { ! alpha53( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ), skol12( X, Y, U, T ) ), T ) ) }.
% 1.32/1.74 { ! alpha53( X, Y, Z, T ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ), skol12( X, Y, Z, T ) ), Z ) ) }.
% 1.32/1.74 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 1.32/1.74 , U ), Y ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ), U ), T ) ), hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), U ), Z ) ), alpha53
% 1.32/1.74 ( X, Y, Z, T ) }.
% 1.32/1.74 { ! alpha48( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! alpha48( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha48( X, Y, Z
% 1.32/1.74 ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol13( X, Y ) ) }.
% 1.32/1.74 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol14( Z, Y ) ) ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 1.32/1.74 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 1.32/1.74 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Int_Oint, skol14( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 1.32/1.74 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 1.32/1.74 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 1.32/1.74 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 1.32/1.74 ) ) }.
% 1.32/1.74 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.32/1.74 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol15( Z, Y
% 1.32/1.74 ), Y ) }.
% 1.32/1.74 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.32/1.74 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.32/1.74 skol15( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 1.32/1.74 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.32/1.74 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 1.32/1.74 , skol15( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.32/1.74 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 1.32/1.74 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.32/1.74 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.32/1.74 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 1.32/1.74 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 1.32/1.74 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.32/1.74 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Omono( tc_Nat_Onat, X
% 1.32/1.74 , c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), T ), Z ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Nat_Onat, Z, Y ), X ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Nat_Onat, X, Z ), Y ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Nat_Onat, Z, X ), Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.32/1.74 tc_Nat_Onat, X, Y ), Y ) = X }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.32/1.74 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 1.32/1.74 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Nat_Onat, Z, X ), Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.32/1.74 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.32/1.74 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.32/1.74 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.74 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 1.32/1.74 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.32/1.74 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.32/1.74 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.32/1.74 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.32/1.74 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Nat_Onat, Y, X ), Y ) = X }.
% 1.32/1.74 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Nat_Onat, Y, X ), X ) = Y }.
% 1.32/1.74 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 1.32/1.74 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 1.32/1.74 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.74 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.32/1.74 Z ) ), Y ) ) }.
% 1.32/1.74 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.74 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.32/1.74 W ) ), U ), Y ) }.
% 1.32/1.74 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.32/1.74 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.32/1.74 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.74 ( X ), Z ), U ), Y ) }.
% 1.32/1.74 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.74 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.32/1.74 Z ) ), U ), T ) = Y }.
% 1.32/1.74 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.32/1.74 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.74 ( X ), Z ), U ), Y ) }.
% 1.32/1.74 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.32/1.74 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.32/1.74 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.32/1.74 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.32/1.74 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 1.32/1.74 X, Y ) ) }.
% 1.32/1.74 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.32/1.74 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.32/1.74 X, Z, Y ) }.
% 1.32/1.74 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 1.32/1.74 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 1.32/1.74 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.32/1.74 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 1.32/1.74 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 1.32/1.74 , Y ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.32/1.74 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.32/1.74 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.32/1.74 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 1.32/1.74 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 1.32/1.74 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.32/1.74 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.32/1.74 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.32/1.74 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.32/1.74 ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.32/1.74 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 1.32/1.74 ) }.
% 1.32/1.74 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), ! hBOOL( hAPP(
% 1.32/1.74 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), hBOOL( hAPP( hAPP
% 1.32/1.74 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 1.32/1.74 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), ! hBOOL( hAPP(
% 1.32/1.74 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), hBOOL( hAPP( hAPP
% 1.32/1.74 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.32/1.74 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.32/1.74 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.32/1.74 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.32/1.74 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.32/1.74 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 1.32/1.74 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 1.32/1.74 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 1.32/1.74 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 1.32/1.74 hAPP( Z, Y ) ) }.
% 1.32/1.74 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.32/1.74 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.32/1.74 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.32/1.74 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.32/1.74 ( tc_Nat_Onat, Z, Y ), X ) }.
% 1.32/1.74 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.32/1.74 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.32/1.74 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 1.32/1.74 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.32/1.74 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.32/1.74 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.32/1.74 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.32/1.74 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 1.32/1.74 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.32/1.74 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 1.32/1.74 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.32/1.74 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 1.32/1.74 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.32/1.74 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.32/1.74 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.32/1.74 T ) ) ) }.
% 1.32/1.74 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.32/1.74 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.32/1.74 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 1.32/1.74 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.32/1.74 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 1.32/1.74 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 1.32/1.74 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.32/1.74 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.32/1.74 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.32/1.74 ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.32/1.74 ( tc_Nat_Onat, Y, Z ), X ) }.
% 1.32/1.74 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.32/1.74 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.74 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.32/1.74 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.74 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.32/1.74 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.32/1.74 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.32/1.74 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.32/1.74 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.32/1.74 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.32/1.74 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.32/1.74 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.32/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.74 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.32/1.74 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.32/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.74 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.32/1.74 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 1.32/1.74 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.32/1.74 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 1.32/1.74 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.74 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.32/1.74 ) }.
% 1.32/1.74 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.32/1.74 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.32/1.74 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.32/1.74 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.32/1.74 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 1.32/1.74 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.74 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.32/1.74 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.32/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.74 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.32/1.74 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 1.32/1.74 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.32/1.74 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.32/1.74 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.32/1.74 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.32/1.74 X, Y ) }.
% 1.32/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.32/1.74 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( X ) ) }.
% 1.32/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.32/1.74 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.32/1.74 , Z, Y ) }.
% 1.32/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.32/1.74 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.32/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.32/1.74 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.32/1.74 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.32/1.74 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.74 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.74 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 1.32/1.74 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.32/1.74 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.32/1.74 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.74 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.32/1.74 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.32/1.74 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.74 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.74 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 1.32/1.74 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.32/1.74 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.32/1.74 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.74 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.32/1.74 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.74 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.32/1.74 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.32/1.74 X, W, Z ) ), U ), T ), Y ) }.
% 1.32/1.74 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.74 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.32/1.74 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.74 ( X ), Z ), U ), Y ) ) }.
% 1.32/1.74 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.74 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.32/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 1.32/1.74 ( X, Z, W ) ), U ), Y ) ) }.
% 1.32/1.74 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.32/1.74 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.32/1.74 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.74 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.32/1.74 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.32/1.74 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.32/1.74 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 1.32/1.74 .
% 1.32/1.74 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.32/1.74 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X, U, T
% 1.32/1.74 ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.32/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.32/1.74 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( X, U, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ), hBOOL( hAPP(
% 1.32/1.74 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X
% 1.32/1.74 , U, T ) ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.32/1.74 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X, U, T
% 1.32/1.74 ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.32/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.32/1.74 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( X, U, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ), hBOOL( hAPP(
% 1.32/1.74 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X
% 1.32/1.74 , U, T ) ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.32/1.74 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 1.32/1.74 ) ) = X }.
% 1.32/1.74 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.32/1.74 , ! alpha12( X, Y, Z ) }.
% 1.32/1.74 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.32/1.74 , ! alpha26( X, Y, Z ) }.
% 1.32/1.74 { alpha12( X, Y, Z ), alpha26( X, Y, Z ), hBOOL( hAPP( Z,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.32/1.74 { ! alpha26( X, Y, Z ), ! hBOOL( hAPP( Z, skol16( T, U, Z ) ) ) }.
% 1.32/1.74 { ! alpha26( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.32/1.74 skol16( X, Y, Z ) ) }.
% 1.32/1.74 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 1.32/1.74 ) ), alpha26( X, Y, Z ) }.
% 1.32/1.74 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.32/1.74 }.
% 1.32/1.74 { ! alpha12( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Nat_Onat ) ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha12( X, Y, Z ) }.
% 1.32/1.74 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.32/1.74 , alpha13( X, Y, Z ) }.
% 1.32/1.74 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.32/1.74 , alpha27( X, Y, Z ) }.
% 1.32/1.74 { ! alpha13( X, Y, Z ), ! alpha27( X, Y, Z ), hBOOL( hAPP( Z,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.32/1.74 { ! alpha27( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.32/1.74 T ), hBOOL( hAPP( Z, T ) ) }.
% 1.32/1.74 { ! hBOOL( hAPP( Z, skol17( T, U, Z ) ) ), alpha27( X, Y, Z ) }.
% 1.32/1.74 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol17( X, Y, Z ) ),
% 1.32/1.74 alpha27( X, Y, Z ) }.
% 1.32/1.74 { ! alpha13( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.32/1.74 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.32/1.74 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha13( X, Y, Z ) }
% 1.32/1.74 .
% 1.32/1.74 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha13
% 1.32/1.74 ( X, Y, Z ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.32/1.74 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.32/1.74 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 1.32/1.74 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 1.32/1.74 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 1.32/1.74 tc_Nat_Onat ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.32/1.74 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.32/1.74 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 1.32/1.74 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 1.32/1.74 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.32/1.74 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.32/1.74 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.32/1.74 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.32/1.74 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.32/1.74 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.32/1.74 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.74 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.32/1.74 ( tc_Nat_Onat ) ) ), X ) ) }.
% 1.32/1.74 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.32/1.74 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 1.32/1.74 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.32/1.74 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.32/1.74 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.32/1.74 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.32/1.74 ( tc_Nat_Onat ) ) ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 1.32/1.74 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 1.32/1.74 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.32/1.74 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.32/1.74 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.32/1.74 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.32/1.74 c_Groups_Oone__class_Oone( X ) }.
% 1.32/1.74 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.32/1.74 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.32/1.74 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.32/1.74 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.32/1.74 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.32/1.74 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 1.32/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.32/1.74 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 1.32/1.74 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 1.32/1.74 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.32/1.74 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 1.32/1.74 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.32/1.74 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 1.32/1.74 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.32/1.74 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.32/1.74 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.32/1.74 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.32/1.74 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 1.32/1.74 }.
% 1.32/1.74 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.32/1.74 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.32/1.74 T ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.74 c_Polynomial_Odegree( X, c_Groups_Ominus__class_Ominus(
% 1.32/1.74 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 1.32/1.74 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.32/1.74 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.32/1.74 tc_Polynomial_Opoly( X ), Y ) }.
% 1.32/1.74 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) ), ! hBOOL( hAPP(
% 1.32/1.74 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ), hBOOL( hAPP(
% 1.32/1.74 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.32/1.74 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 1.32/1.74 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.32/1.74 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.32/1.74 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.32/1.74 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.32/1.74 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.32/1.74 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.32/1.74 .
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.32/1.74 ( tc_Int_Oint ) ) ) }.
% 1.32/1.74 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.32/1.74 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 1.32/1.74 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.32/1.74 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.74 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 1.32/1.74 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 1.32/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.32/1.74 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha14( X, Y ) }.
% 1.32/1.74 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.32/1.74 { ! alpha14( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.32/1.74 { ! alpha14( X, Y ), alpha28( X, Y ), alpha35( X, Y ) }.
% 1.32/1.74 { ! alpha28( X, Y ), alpha14( X, Y ) }.
% 1.32/1.74 { ! alpha35( X, Y ), alpha14( X, Y ) }.
% 1.32/1.74 { ! alpha35( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.32/1.74 { ! alpha35( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha35( X, Y ) }.
% 1.32/1.74 { ! alpha28( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.32/1.74 { ! alpha28( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha28( X, Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Int_Oint, Y, X ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 1.32/1.74 , Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 1.32/1.74 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Int_Oint, Y, X ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Int_Oint ), Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Int_Oint, X, Y ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.32/1.74 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 1.32/1.74 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Int_Oint, Y, X ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.32/1.74 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.32/1.74 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Int_Oint, X, Y ), X ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 1.32/1.74 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Int_Oint, Z, Y ), X ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), c_Divides_Odiv__class_Odiv( X
% 1.32/1.74 , c_Groups_Oplus__class_Oplus( X, Y, T ), Z ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Y, Z ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Int_Oint, X, Y ) ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.74 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.32/1.74 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.74 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.32/1.74 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.74 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.74 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 1.32/1.74 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.74 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.32/1.74 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), c_Divides_Odiv__class_Odiv( X, Y
% 1.32/1.74 , Z ) ) = Y }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Odiv( X, Y
% 1.32/1.74 , Z ) ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.32/1.74 ), Z ) = Y }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.32/1.74 ), T ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), U ), T ) ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.32/1.74 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 1.32/1.74 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.32/1.74 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Int_Oint ), Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.32/1.74 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.74 }.
% 1.32/1.74 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.32/1.74 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 1.32/1.74 c_Power_Opower__class_Opower( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.32/1.74 ), T ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.32/1.74 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.74 c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), c_Divides_Odiv__class_Odiv( X, Y, Z ) ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( X, T, Z ) ) ), hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), c_Divides_Odiv__class_Odiv( X, Y, Z ) ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( X, T, Z ) ) ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.32/1.74 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.32/1.74 { ! class_Divides_Oring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Odiv( X
% 1.32/1.74 , Y, c_Groups_Ouminus__class_Ouminus( X, Z ) ) =
% 1.32/1.74 c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.32/1.74 ) }.
% 1.32/1.74 { ! class_Divides_Oring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Odiv( X
% 1.32/1.74 , c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) =
% 1.32/1.74 c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.32/1.74 ) }.
% 1.32/1.74 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.32/1.74 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) }.
% 1.32/1.74 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y,
% 1.32/1.74 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.32/1.74 ( tc_Int_Oint, Y ), X ) }.
% 1.32/1.74 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 1.32/1.74 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.74 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 1.32/1.74 }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.74 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 1.32/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 1.32/1.74 ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.74 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 1.32/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 1.32/1.74 ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.74 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 1.32/1.74 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 1.32/1.74 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.74 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 1.32/1.74 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 1.32/1.74 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.74 , Z = c_Groups_Ozero__class_Ozero( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), U ) ), ! c_Divides_Odiv__class_Odiv(
% 1.32/1.74 X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.74 , Z = c_Groups_Ozero__class_Ozero( X ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), ! hBOOL( hAPP( hAPP(
% 1.32/1.74 c_Rings_Odvd__class_Odvd( X ), Z ), U ) ), ! hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 1.32/1.74 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.74 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z ) ), !
% 1.32/1.74 c_Divides_Odiv__class_Odiv( X, Z, Y ) = T, Z = hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.74 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z ) ), ! Z =
% 1.32/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( X, Z, Y ) = T }.
% 1.32/1.74 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.32/1.74 alpha15( X, Z ) }.
% 1.32/1.74 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.32/1.74 alpha29( X, Y, Z ) }.
% 1.32/1.74 { ! alpha15( X, Z ), ! alpha29( X, Y, Z ), hBOOL( hAPP( Z,
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 1.32/1.74 { ! alpha29( X, Y, Z ), alpha36( X, Y, Z ) }.
% 1.32/1.74 { ! alpha29( X, Y, Z ), alpha39( X, Y, Z ) }.
% 1.32/1.74 { ! alpha36( X, Y, Z ), ! alpha39( X, Y, Z ), alpha29( X, Y, Z ) }.
% 1.32/1.74 { ! alpha39( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha42( X, Y, Z ) }.
% 1.32/1.74 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha39( X, Y, Z ) }.
% 1.32/1.74 { ! alpha42( X, Y, Z ), alpha39( X, Y, Z ) }.
% 1.32/1.74 { ! alpha42( X, Y, Z ), ! alpha44( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.32/1.74 { ! hBOOL( hAPP( Z, skol18( T, U, Z ) ) ), alpha42( X, Y, Z ) }.
% 1.32/1.74 { alpha44( X, Y, skol18( X, Y, Z ) ), alpha42( X, Y, Z ) }.
% 1.32/1.74 { ! alpha44( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.32/1.74 skol19( X, T, U ) ) }.
% 1.32/1.74 { ! alpha44( X, Y, Z ), alpha46( X, Y, Z, skol19( X, Y, Z ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha46( X, Y, Z
% 1.32/1.74 , T ), alpha44( X, Y, Z ) }.
% 1.32/1.74 { ! alpha46( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.32/1.74 { ! alpha46( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.32/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.32/1.74 .
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha46( X,
% 1.32/1.74 Y, Z, T ) }.
% 1.32/1.74 { ! alpha36( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha40( X, Y, Z ) }.
% 1.32/1.74 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Int_Oint ), X ), alpha36( X, Y, Z ) }.
% 1.32/1.74 { ! alpha40( X, Y, Z ), alpha36( X, Y, Z ) }.
% 1.32/1.74 { ! alpha40( X, Y, Z ), ! alpha43( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.32/1.74 { ! hBOOL( hAPP( Z, skol20( T, U, Z ) ) ), alpha40( X, Y, Z ) }.
% 1.32/1.74 { alpha43( X, Y, skol20( X, Y, Z ) ), alpha40( X, Y, Z ) }.
% 1.32/1.74 { ! alpha43( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol21( T, U, W ) ) }.
% 1.32/1.74 { ! alpha43( X, Y, Z ), alpha45( X, Y, Z, skol21( X, Y, Z ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha45( X, Y, Z, T )
% 1.32/1.74 , alpha43( X, Y, Z ) }.
% 1.32/1.74 { ! alpha45( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 1.32/1.74 ) }.
% 1.32/1.74 { ! alpha45( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.32/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.32/1.74 .
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha45( X,
% 1.32/1.74 Y, Z, T ) }.
% 1.32/1.74 { ! alpha15( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.32/1.74 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.32/1.74 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha15( X, Y ) }.
% 1.32/1.74 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha15
% 1.32/1.74 ( X, Y ) }.
% 1.32/1.74 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha49( X,
% 1.32/1.74 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Int_Oint, T, Z ) = Y }.
% 1.32/1.74 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha49( X,
% 1.32/1.74 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Int_Oint, T, Z ) = Y }.
% 1.32/1.74 { ! alpha49( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.32/1.74 { ! alpha49( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha49( X, Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 1.32/1.74 , alpha49( X, Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3div( X, Y ) =
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) }.
% 1.32/1.74 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3div( X, Y ) =
% 1.32/1.74 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 1.32/1.74 ( tc_Int_Oint, X, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) }
% 1.32/1.74 .
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.32/1.74 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.32/1.74 tc_Int_Oint, X, Y ) }.
% 1.32/1.74 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.32/1.74 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 1.32/1.74 ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 1.32/1.74 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.32/1.74 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.32/1.74 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.32/1.74 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.32/1.74 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Nat_Onat, Y, X ), Y ) }.
% 1.32/1.74 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) }.
% 1.32/1.74 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.74 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Nat_Onat, Z, Y ), X ) }.
% 1.32/1.74 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 1.32/1.74 tc_Polynomial_Opoly( X ), Y ) ) = c_Groups_Ouminus__class_Ouminus(
% 1.32/1.74 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.32/1.74 ( X ), Z, Y ) ) }.
% 1.32/1.74 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 1.32/1.74 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.32/1.74 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.32/1.74 ( X ), Z, Y ) ) }.
% 1.32/1.74 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.32/1.74 ( X ), T, Z ), Y ) }.
% 1.32/1.74 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.74 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 1.32/1.74 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 1.32/1.74 , c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 1.32/1.74 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.32/1.74 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ) =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.32/1.74 ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.32/1.74 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.32/1.74 tc_Nat_Onat, Y, X ), X ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.32/1.74 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.32/1.74 tc_Nat_Onat, Y, X ), X ) ) }.
% 1.32/1.74 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.32/1.74 alpha16( X, Z ) }.
% 1.32/1.74 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.32/1.74 alpha30( X, Y, Z ) }.
% 1.32/1.74 { ! alpha16( X, Z ), ! alpha30( X, Y, Z ), hBOOL( hAPP( Z,
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 1.32/1.74 { ! alpha30( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.32/1.74 alpha37( X, Y, Z ) }.
% 1.32/1.74 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha30( X, Y, Z ) }.
% 1.32/1.74 { ! alpha37( X, Y, Z ), alpha30( X, Y, Z ) }.
% 1.32/1.74 { ! alpha37( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 1.32/1.74 ), alpha41( X, Y, Z, T ) }.
% 1.32/1.74 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol22( X, T, U ), X ),
% 1.32/1.74 alpha37( X, Y, Z ) }.
% 1.32/1.74 { ! alpha41( X, Y, Z, skol22( X, Y, Z ) ), alpha37( X, Y, Z ) }.
% 1.32/1.74 { ! alpha41( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.32/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.32/1.74 hBOOL( hAPP( Z, U ) ) }.
% 1.32/1.74 { ! hBOOL( hAPP( Z, skol23( U, W, Z, V0 ) ) ), alpha41( X, Y, Z, T ) }.
% 1.32/1.74 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol23( X, Y, Z, T ) )
% 1.32/1.74 , T ), alpha41( X, Y, Z, T ) }.
% 1.32/1.74 { ! alpha16( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.32/1.74 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.32/1.74 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha16( X, Y ) }.
% 1.32/1.74 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha16
% 1.32/1.74 ( X, Y ) }.
% 1.32/1.74 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.32/1.74 alpha17( X, Z ), alpha31( X, Y, Z ) }.
% 1.32/1.74 { ! alpha17( X, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Nat_Onat, Y, X ) ) ) }.
% 1.32/1.74 { ! alpha31( X, Y, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Nat_Onat, Y, X ) ) ) }.
% 1.32/1.74 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol24( X
% 1.32/1.74 , Y, T ) ), Y ) }.
% 1.32/1.74 { ! alpha31( X, Y, Z ), alpha38( X, Y, Z, skol24( X, Y, Z ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), T ), Y ), ! alpha38( X
% 1.32/1.74 , Y, Z, T ), alpha31( X, Y, Z ) }.
% 1.32/1.74 { ! alpha38( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.32/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc
% 1.32/1.74 ( T ) ) ) }.
% 1.32/1.74 { ! alpha38( X, Y, Z, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( T ) ) ), !
% 1.32/1.74 hBOOL( hAPP( Z, T ) ), alpha38( X, Y, Z, T ) }.
% 1.32/1.74 { ! alpha17( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.32/1.74 { ! alpha17( X, Y ), hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Nat_Onat ) ) ) }.
% 1.32/1.74 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( Y,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha17( X, Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.32/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ),
% 1.32/1.74 ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ), Z
% 1.32/1.74 = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 1.32/1.74 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 1.32/1.74 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ) }
% 1.32/1.74 .
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 1.32/1.74 , Y ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.32/1.74 tc_Nat_Onat, Y, X ), X ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 1.32/1.74 ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.32/1.74 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.32/1.74 tc_Int_Oint, X, Y ) }.
% 1.32/1.74 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.32/1.74 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 1.32/1.74 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 1.32/1.74 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 1.32/1.74 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 1.32/1.74 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 1.32/1.74 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 1.32/1.74 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.32/1.74 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 1.32/1.74 ( X ) ) ) }.
% 1.32/1.74 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 1.32/1.74 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.32/1.74 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 1.32/1.74 .
% 1.32/1.74 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.32/1.74 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 1.32/1.74 c_Groups_Oone__class_Oone( X ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 1.32/1.74 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 1.32/1.74 .
% 1.32/1.74 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.32/1.74 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.32/1.74 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.32/1.74 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 1.32/1.74 }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 1.32/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 1.32/1.74 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 1.32/1.74 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.74 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 1.32/1.74 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 1.32/1.74 ) }.
% 1.32/1.74 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.32/1.74 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.74 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 1.32/1.74 c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 1.32/1.74 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.74 }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.32/1.74 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.32/1.74 }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.32/1.74 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.32/1.74 .
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.32/1.74 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 1.32/1.74 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 1.32/1.74 .
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.32/1.74 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.32/1.74 .
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.32/1.74 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.32/1.74 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.32/1.74 .
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 1.32/1.74 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.32/1.74 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 1.32/1.74 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.32/1.74 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 1.32/1.74 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.32/1.74 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.74 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.32/1.74 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.32/1.74 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.32/1.74 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.32/1.74 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.32/1.74 c_Groups_Oone__class_Oone( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 1.32/1.74 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 1.32/1.74 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.32/1.74 .
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.32/1.74 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 1.32/1.74 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 1.32/1.74 }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.32/1.74 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 1.32/1.74 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 1.32/1.74 }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol25( Z, Y ) ) ), !
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 1.32/1.74 , hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, U, hAPP(
% 1.32/1.74 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 1.32/1.74 tc_Int_Oint, skol25( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 1.32/1.74 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 1.32/1.74 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 1.32/1.74 tc_Int_Oint, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.32/1.74 , Z ), X ) ) ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.32/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha18( X, Y, T,
% 1.32/1.74 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha18( X, Y, skol26( X, Y
% 1.32/1.74 , Z ), skol28( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.32/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 1.32/1.74 skol26( X, Y, Z ) ), skol28( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.32/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.32/1.74 { ! alpha18( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T
% 1.32/1.74 ) }.
% 1.32/1.74 { ! alpha18( X, Y, Z, T ), alpha32( X, Y, Z, T ) }.
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha32( X, Y, Z
% 1.32/1.74 , T ), alpha18( X, Y, Z, T ) }.
% 1.32/1.74 { ! alpha32( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.32/1.74 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.32/1.74 { ! alpha32( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.32/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.32/1.74 .
% 1.32/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha32( X,
% 1.32/1.74 Y, Z, T ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.74 ( X ), c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ),
% 1.32/1.74 c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.32/1.74 ( X ), T ), c_Divides_Odiv__class_Odiv( X, Z, T ) ),
% 1.32/1.74 c_Divides_Odiv__class_Omod( X, Z, T ) ), Y ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.32/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X
% 1.32/1.74 , Z, Y ) ), Y ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.32/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), c_Divides_Odiv__class_Omod( X, Y
% 1.32/1.74 , Z ) ) = Y }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 1.32/1.74 c_Divides_Odiv__class_Omod( X, Z, Y ), hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 1.32/1.74 ), Y ) ) = Z }.
% 1.32/1.74 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.32/1.74 tc_Int_Oint, Z, X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.32/1.74 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, X ),
% 1.32/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.32/1.74 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 1.32/1.74 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.32/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.32/1.74 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 1.32/1.74 ( X ) }.
% 1.32/1.74 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.32/1.74 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 1.32/1.74 tc_Int_Oint ) ) = X }.
% 1.32/1.74 { Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.32/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 1.32/1.74 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 1.32/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.32/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.32/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.32/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.32/1.74 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.32/1.74 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.32/1.74 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 1.32/1.74 ( tc_fun( Y, X ) ) }.
% 1.32/1.74 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.32/1.74 ) ) }.
% 1.32/1.74 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.32/1.74 .
% 1.32/1.74 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.32/1.74 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 1.32/1.74 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 1.32/1.74 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.32/1.74 tc_Int_Oint ) }.
% 1.32/1.74 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.32/1.74 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.32/1.74 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.32/1.74 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.32/1.74 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.32/1.74 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.32/1.74 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.32/1.74 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.32/1.74 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.32/1.74 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.32/1.74 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.32/1.74 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.32/1.74 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.32/1.74 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.32/1.74 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.32/1.74 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.32/1.74 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.32/1.74 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.32/1.74 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.32/1.74 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.32/1.74 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.32/1.74 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.32/1.74 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.32/1.74 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 1.32/1.74 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.32/1.74 { class_Groups_Ominus( tc_Int_Oint ) }.
% 1.32/1.74 { class_Power_Opower( tc_Int_Oint ) }.
% 1.32/1.74 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.32/1.74 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.32/1.74 { class_Rings_Odvd( tc_Int_Oint ) }.
% 1.32/1.74 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.32/1.74 tc_Nat_Onat ) }.
% 1.32/1.74 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 1.32/1.74 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 1.32/1.74 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.32/1.74 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.32/1.74 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.32/1.74 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 1.32/1.74 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 1.32/1.74 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.32/1.74 tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 1.32/1.74 { ! class_Rings_Oidom( X ),
% 1.32/1.74 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.32/1.74 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.32/1.74 ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.32/1.74 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.32/1.74 X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.32/1.74 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.32/1.74 ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.32/1.74 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.32/1.74 }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.32/1.74 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.32/1.74 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.32/1.74 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.32/1.74 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.32/1.74 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.32/1.74 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.32/1.74 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.32/1.74 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.32/1.74 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.32/1.74 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.32/1.74 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.32/1.74 ( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.32/1.74 ( tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 1.32/1.74 ( X ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.32/1.74 }.
% 1.32/1.74 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.32/1.74 ) ) }.
% 1.32/1.74 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.32/1.74 .
% 1.32/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 1.32/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.32/1.74 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 1.32/1.74 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 1.32/1.74 { ! v_qa____ = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.32/1.74 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), c_Polynomial_OpCons(
% 1.32/1.74 tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex
% 1.32/1.74 , v_a____ ), c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 1.32/1.74 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 1.32/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 1.32/1.74 ) ) ), X ), v_thesis____ }.
% 1.32/1.74 { ! v_thesis____ }.
% 1.32/1.74
% 1.32/1.74 *** allocated 15000 integers for clauses
% 1.32/1.74 *** allocated 22500 integers for clauses
% 1.32/1.74 *** allocated 33750 integers for clauses
% 1.32/1.74 *** allocated 50625 integers for clauses
% 1.32/1.74 *** allocated 75937 integers for clauses
% 1.32/1.74 percentage equality = 0.261993, percentage horn = 0.901500
% 1.32/1.74 This is a problem with some equality
% 1.32/1.74
% 1.32/1.74
% 1.32/1.74
% 1.32/1.74 Options Used:
% 1.32/1.74
% 1.32/1.74 useres = 1
% 1.32/1.74 useparamod = 1
% 1.32/1.74 useeqrefl = 1
% 1.32/1.74 useeqfact = 1
% 1.32/1.74 usefactor = 1
% 1.32/1.74 usesimpsplitting = 0
% 1.32/1.74 usesimpdemod = 5
% 1.32/1.74 usesimpres = 3
% 1.32/1.74
% 1.32/1.74 resimpinuse = 1000
% 1.32/1.74 resimpclauses = 20000
% 1.32/1.74 substype = eqrewr
% 1.32/1.74 backwardsubs = 1
% 1.32/1.74 selectoldest = 5
% 1.32/1.74
% 1.32/1.74 litorderings [0] = split
% 1.32/1.74 litorderings [1] = extend the termordering, first sorting on arguments
% 1.32/1.74
% 1.32/1.74 termordering = kbo
% 1.32/1.74
% 1.32/1.74 litapriori = 0
% 1.32/1.74 termapriori = 1
% 1.32/1.74 litaposteriori = 0
% 1.32/1.74 termaposteriori = 0
% 1.32/1.74 demodaposteriori = 0
% 1.32/1.74 ordereqreflfact = 0
% 1.32/1.74
% 1.32/1.74 litselect = negord
% 1.32/1.74
% 1.32/1.74 maxweight = 15
% 1.32/1.74 maxdepth = 30000
% 1.32/1.74 maxlength = 115
% 1.32/1.74 maxnrvars = 195
% 1.32/1.74 excuselevel = 1
% 1.32/1.74 increasemaxweight = 1
% 1.32/1.74
% 1.32/1.74 maxselected = 10000000
% 1.32/1.74 maxnrclauses = 10000000
% 1.32/1.74
% 1.32/1.74 showgenerated = 0
% 1.32/1.74 showkept = 0
% 1.32/1.74 showselected = 0
% 1.32/1.74 showdeleted = 0
% 1.32/1.74 showresimp = 1
% 1.32/1.74 showstatus = 2000
% 1.32/1.74
% 1.32/1.74 prologoutput = 0
% 1.32/1.74 nrgoals = 5000000
% 1.32/1.74 totalproof = 1
% 1.32/1.74
% 1.32/1.74 Symbols occurring in the translation:
% 1.32/1.74
% 1.32/1.74 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.32/1.74 . [1, 2] (w:1, o:190, a:1, s:1, b:0),
% 1.32/1.74 ! [4, 1] (w:0, o:109, a:1, s:1, b:0),
% 1.32/1.74 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.32/1.74 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.32/1.74 hAPP [38, 2] (w:1, o:214, a:1, s:1, b:0),
% 1.32/1.74 v_qa____ [39, 0] (w:1, o:14, a:1, s:1, b:0),
% 1.32/1.74 tc_Complex_Ocomplex [40, 0] (w:1, o:15, a:1, s:1, b:0),
% 1.32/1.74 tc_Polynomial_Opoly [41, 1] (w:1, o:115, a:1, s:1, b:0),
% 1.32/1.74 c_Groups_Ozero__class_Ozero [42, 1] (w:1, o:116, a:1, s:1, b:0),
% 1.32/1.74 c_Rings_Odvd__class_Odvd [43, 1] (w:1, o:117, a:1, s:1, b:0),
% 1.32/1.74 v_a____ [44, 0] (w:1, o:16, a:1, s:1, b:0),
% 1.32/1.74 c_Groups_Ouminus__class_Ouminus [45, 2] (w:1, o:216, a:1, s:1, b:0),
% 1.32/1.74
% 1.32/1.74 c_Groups_Oone__class_Oone [46, 1] (w:1, o:118, a:1, s:1, b:0),
% 1.32/1.74 c_Polynomial_OpCons [47, 3] (w:1, o:252, a:1, s:1, b:0),
% 1.32/1.74 hBOOL [48, 1] (w:1, o:119, a:1, s:1, b:0),
% 1.32/1.74 class_Rings_Ocomm__semiring__1 [50, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.32/1.74 class_Groups_Ozero [51, 1] (w:1, o:125, a:1, s:1, b:0),
% 1.32/1.74 class_Rings_Ocomm__ring__1 [55, 1] (w:1, o:120, a:1, s:1, b:0),
% 1.32/1.74 c_Groups_Otimes__class_Otimes [56, 1] (w:1, o:126, a:1, s:1, b:0),
% 1.32/1.74 class_Rings_Oring__1__no__zero__divisors [58, 1] (w:1, o:127, a:1, s:
% 1.32/1.74 1, b:0),
% 1.32/1.74 class_Rings_Ocomm__semiring__0 [60, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.32/1.74 class_Groups_Oab__group__add [63, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.32/1.74 v_pa____ [65, 0] (w:1, o:12, a:1, s:1, b:0),
% 1.32/1.74 class_Rings_Oring [67, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.32/1.74 v_na____ [68, 0] (w:1, o:35, a:1, s:1, b:0),
% 1.32/1.74 tc_Nat_Onat [69, 0] (w:1, o:36, a:1, s:1, b:0),
% 1.32/1.74 c_Polynomial_Oorder [70, 3] (w:1, o:251, a:1, s:1, b:0),
% 1.32/1.74 c_Polynomial_Opoly [71, 2] (w:1, o:217, a:1, s:1, b:0),
% 1.32/1.74 class_Rings_Odvd [74, 1] (w:1, o:131, a:1, s:1, b:0),
% 1.32/1.74 class_Rings_Oidom [79, 1] (w:1, o:132, a:1, s:1, b:0),
% 1.32/1.74 class_Rings_Ono__zero__divisors [85, 1] (w:1, o:143, a:1, s:1, b:0),
% 1.32/1.74
% 1.32/1.74 class_Rings_Oring__no__zero__divisors [86, 1] (w:1, o:144, a:1, s:1
% 1.32/1.74 , b:0),
% 1.32/1.74 class_Rings_Omult__zero [87, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.32/1.74 class_Rings_Ozero__neq__one [88, 1] (w:1, o:145, a:1, s:1, b:0),
% 1.32/1.74 c_Power_Opower__class_Opower [89, 1] (w:1, o:146, a:1, s:1, b:0),
% 1.32/1.74 class_RealVector_Oreal__normed__algebra [91, 1] (w:1, o:147, a:1, s:1
% 1.32/1.74 , b:0),
% 1.32/1.74 class_Groups_Ocomm__monoid__mult [93, 1] (w:1, o:148, a:1, s:1, b:0)
% 1.32/1.74 ,
% 1.32/1.74 class_Groups_Omonoid__mult [94, 1] (w:1, o:150, a:1, s:1, b:0),
% 1.32/1.74 class_Groups_Olinordered__ab__group__add [95, 1] (w:1, o:149, a:1, s:
% 1.32/1.74 1, b:0),
% 1.32/1.74 class_Groups_Ogroup__add [96, 1] (w:1, o:151, a:1, s:1, b:0),
% 1.32/1.74 v_n [97, 0] (w:1, o:59, a:1, s:1, b:0),
% 1.32/1.74 v_p [98, 0] (w:1, o:13, a:1, s:1, b:0),
% 1.32/1.74 v_q [99, 0] (w:1, o:60, a:1, s:1, b:0),
% 1.32/1.74 c_Polynomial_Odegree [100, 2] (w:1, o:219, a:1, s:1, b:0),
% 1.32/1.74 class_Int_Oring__char__0 [101, 1] (w:1, o:152, a:1, s:1, b:0),
% 1.32/1.74 class_Rings_Ocomm__ring [103, 1] (w:1, o:121, a:1, s:1, b:0),
% 1.32/1.74 class_Groups_Oab__semigroup__mult [104, 1] (w:1, o:153, a:1, s:1, b:0
% 1.32/1.74 ),
% 1.32/1.74 class_Groups_Oone [105, 1] (w:1, o:154, a:1, s:1, b:0),
% 1.32/1.74 c_Nat_OSuc [106, 1] (w:1, o:155, a:1, s:1, b:0),
% 1.32/1.74 c_Orderings_Oord__class_Oless__eq [107, 3] (w:1, o:249, a:1, s:1, b:0
% 1.32/1.74 ),
% 1.32/1.74 class_Rings_Oring__1 [108, 1] (w:1, o:156, a:1, s:1, b:0),
% 1.32/1.74 class_Power_Opower [109, 1] (w:1, o:161, a:1, s:1, b:0),
% 1.32/1.74 class_Rings_Osemiring__0 [110, 1] (w:1, o:162, a:1, s:1, b:0),
% 1.32/1.74 class_Rings_Olinordered__semidom [114, 1] (w:1, o:135, a:1, s:1, b:0)
% 1.32/1.74 ,
% 1.32/1.74 class_Groups_Oordered__ab__group__add [116, 1] (w:1, o:163, a:1, s:1
% 1.32/1.74 , b:0),
% 1.32/1.74 class_Rings_Oordered__cancel__semiring [118, 1] (w:1, o:164, a:1, s:1
% 1.32/1.74 , b:0),
% 1.32/1.74 class_Rings_Oordered__ring [119, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.32/1.74 class_Rings_Oordered__semiring [120, 1] (w:1, o:166, a:1, s:1, b:0),
% 1.32/1.74
% 1.32/1.74 class_Rings_Oordered__comm__semiring [121, 1] (w:1, o:167, a:1, s:1
% 1.32/1.74 , b:0),
% 1.32/1.74 class_Rings_Olinordered__ring__strict [122, 1] (w:1, o:133, a:1, s:1
% 1.32/1.74 , b:0),
% 1.32/1.74 class_Rings_Olinordered__ring [123, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.32/1.74 class_Rings_Olinordered__idom [124, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.32/1.74 c_Orderings_Oord__class_Oless [127, 3] (w:1, o:250, a:1, s:1, b:0),
% 1.32/1.74 class_Rings_Olinordered__semiring__strict [137, 1] (w:1, o:137, a:1
% 1.32/1.74 , s:1, b:0),
% 1.32/1.74 class_Rings_Olinordered__comm__semiring__strict [138, 1] (w:1, o:138
% 1.32/1.74 , a:1, s:1, b:0),
% 1.32/1.74 class_Rings_Olinordered__semiring [139, 1] (w:1, o:139, a:1, s:1, b:0
% 1.32/1.74 ),
% 1.32/1.74 tc_Int_Oint [145, 0] (w:1, o:90, a:1, s:1, b:0),
% 1.32/1.74 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [146, 2] (w:1, o:
% 1.32/1.74 215, a:1, s:1, b:0),
% 1.32/1.74 class_Orderings_Opreorder [147, 1] (w:1, o:159, a:1, s:1, b:0),
% 1.32/1.74 c_Power_Opower_Opower [148, 3] (w:1, o:253, a:1, s:1, b:0),
% 1.32/1.74 c_Polynomial_Opcompose [149, 3] (w:1, o:254, a:1, s:1, b:0),
% 1.32/1.74 class_Orderings_Olinorder [152, 1] (w:1, o:160, a:1, s:1, b:0),
% 1.32/1.74 class_Orderings_Oord [153, 1] (w:1, o:157, a:1, s:1, b:0),
% 1.32/1.74 tc_fun [154, 2] (w:1, o:229, a:1, s:1, b:0),
% 1.32/1.74 class_Orderings_Oorder [155, 1] (w:1, o:158, a:1, s:1, b:0),
% 1.32/1.74 c_Polynomial_Opos__poly [156, 2] (w:1, o:230, a:1, s:1, b:0),
% 1.32/1.74 class_Lattices_Oboolean__algebra [157, 1] (w:1, o:169, a:1, s:1, b:0)
% 1.32/1.74 ,
% 1.32/1.74 class_Lattices_Oab__semigroup__idem__mult [158, 1] (w:1, o:168, a:1
% 1.32/1.74 , s:1, b:0),
% 1.32/1.74 class_Groups_Ouminus [160, 1] (w:1, o:170, a:1, s:1, b:0),
% 1.32/1.74 c_Polynomial_Omonom [161, 3] (w:1, o:255, a:1, s:1, b:0),
% 1.32/1.74 c_Polynomial_Opoly__rec [163, 5] (w:1, o:321, a:1, s:1, b:0),
% 1.32/1.74 c_Polynomial_Osynthetic__div [164, 3] (w:1, o:256, a:1, s:1, b:0),
% 1.32/1.74 c_Polynomial_Ocoeff [165, 2] (w:1, o:218, a:1, s:1, b:0),
% 1.32/1.74 c_fequal [172, 2] (w:1, o:231, a:1, s:1, b:0),
% 1.32/1.74 c_If [173, 4] (w:1, o:303, a:1, s:1, b:0),
% 1.32/1.74 c_Groups_Oplus__class_Oplus [175, 3] (w:1, o:257, a:1, s:1, b:0),
% 1.32/1.74 class_Groups_Oordered__ab__semigroup__add__imp__le [176, 1] (w:1, o:
% 1.32/1.74 171, a:1, s:1, b:0),
% 1.32/1.74 class_Groups_Oordered__ab__semigroup__add [177, 1] (w:1, o:172, a:1
% 1.32/1.74 , s:1, b:0),
% 1.32/1.74 class_Groups_Ocomm__monoid__add [178, 1] (w:1, o:173, a:1, s:1, b:0)
% 1.32/1.74 ,
% 1.32/1.74 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 2.36/2.75 179, 1] (w:1, o:178, a:1, s:1, b:0),
% 2.36/2.75 class_Groups_Omonoid__add [180, 1] (w:1, o:179, a:1, s:1, b:0),
% 2.36/2.75 class_Groups_Oordered__cancel__ab__semigroup__add [181, 1] (w:1, o:
% 2.36/2.75 180, a:1, s:1, b:0),
% 2.36/2.75 class_Rings_Osemiring [183, 1] (w:1, o:174, a:1, s:1, b:0),
% 2.36/2.75 class_Rings_Ocomm__semiring [184, 1] (w:1, o:130, a:1, s:1, b:0),
% 2.36/2.75 class_Groups_Ocancel__semigroup__add [189, 1] (w:1, o:181, a:1, s:1
% 2.36/2.75 , b:0),
% 2.36/2.75 class_Groups_Ocancel__ab__semigroup__add [190, 1] (w:1, o:182, a:1
% 2.36/2.75 , s:1, b:0),
% 2.36/2.75 class_Groups_Oab__semigroup__add [191, 1] (w:1, o:183, a:1, s:1, b:0)
% 2.36/2.75 ,
% 2.36/2.75 class_Groups_Oordered__comm__monoid__add [192, 1] (w:1, o:184, a:1
% 2.36/2.75 , s:1, b:0),
% 2.36/2.75 class_Rings_Olinordered__semiring__1 [196, 1] (w:1, o:140, a:1, s:1
% 2.36/2.75 , b:0),
% 2.36/2.75 class_Rings_Olinordered__semiring__1__strict [197, 1] (w:1, o:141, a:
% 2.36/2.75 1, s:1, b:0),
% 2.36/2.75 class_Fields_Ofield [199, 1] (w:1, o:124, a:1, s:1, b:0),
% 2.36/2.75 c_Polynomial_Opdivmod__rel [200, 5] (w:1, o:322, a:1, s:1, b:0),
% 2.36/2.76 c_Polynomial_Opoly__gcd [202, 3] (w:1, o:258, a:1, s:1, b:0),
% 2.36/2.76 c_Groups_Ominus__class_Ominus [212, 3] (w:1, o:259, a:1, s:1, b:0),
% 2.36/2.76 c_Orderings_Oorder_Omono [213, 4] (w:1, o:304, a:1, s:1, b:0),
% 2.36/2.76 class_Groups_Ominus [218, 1] (w:1, o:185, a:1, s:1, b:0),
% 2.36/2.76 c_Divides_Odiv__class_Odiv [222, 3] (w:1, o:260, a:1, s:1, b:0),
% 2.36/2.76 class_Divides_Osemiring__div [223, 1] (w:1, o:187, a:1, s:1, b:0),
% 2.36/2.76 class_Divides_Oring__div [224, 1] (w:1, o:186, a:1, s:1, b:0),
% 2.36/2.76 c_SMT_Oz3div [228, 2] (w:1, o:232, a:1, s:1, b:0),
% 2.36/2.76 c_Nat__Transfer_Otsub [229, 2] (w:1, o:233, a:1, s:1, b:0),
% 2.36/2.76 c_Groups_Osgn__class_Osgn [230, 2] (w:1, o:234, a:1, s:1, b:0),
% 2.36/2.76 class_RealVector_Oreal__normed__vector [231, 1] (w:1, o:175, a:1, s:1
% 2.36/2.76 , b:0),
% 2.36/2.76 class_RealVector_Oreal__normed__algebra__1 [232, 1] (w:1, o:176, a:1
% 2.36/2.76 , s:1, b:0),
% 2.36/2.76 class_RealVector_Oreal__normed__div__algebra [233, 1] (w:1, o:177, a:
% 2.36/2.76 1, s:1, b:0),
% 2.36/2.76 class_Groups_Osgn__if [234, 1] (w:1, o:188, a:1, s:1, b:0),
% 2.36/2.76 c_Divides_Odiv__class_Omod [235, 3] (w:1, o:261, a:1, s:1, b:0),
% 2.36/2.76 class_Groups_Ocancel__comm__monoid__add [237, 1] (w:1, o:189, a:1, s:
% 2.36/2.76 1, b:0),
% 2.36/2.76 tc_HOL_Obool [239, 0] (w:1, o:89, a:1, s:1, b:0),
% 2.36/2.76 v_thesis____ [241, 0] (w:1, o:108, a:1, s:1, b:0),
% 2.36/2.76 alpha1 [242, 3] (w:1, o:262, a:1, s:1, b:1),
% 2.36/2.76 alpha2 [243, 3] (w:1, o:266, a:1, s:1, b:1),
% 2.36/2.76 alpha3 [244, 2] (w:1, o:238, a:1, s:1, b:1),
% 2.36/2.76 alpha4 [245, 2] (w:1, o:240, a:1, s:1, b:1),
% 2.36/2.76 alpha5 [246, 2] (w:1, o:242, a:1, s:1, b:1),
% 2.36/2.76 alpha6 [247, 4] (w:1, o:308, a:1, s:1, b:1),
% 2.36/2.76 alpha7 [248, 4] (w:1, o:309, a:1, s:1, b:1),
% 2.36/2.76 alpha8 [249, 3] (w:1, o:267, a:1, s:1, b:1),
% 2.36/2.76 alpha9 [250, 3] (w:1, o:268, a:1, s:1, b:1),
% 2.36/2.76 alpha10 [251, 2] (w:1, o:243, a:1, s:1, b:1),
% 2.36/2.76 alpha11 [252, 2] (w:1, o:244, a:1, s:1, b:1),
% 2.36/2.76 alpha12 [253, 3] (w:1, o:263, a:1, s:1, b:1),
% 2.36/2.76 alpha13 [254, 3] (w:1, o:264, a:1, s:1, b:1),
% 2.36/2.76 alpha14 [255, 2] (w:1, o:245, a:1, s:1, b:1),
% 2.36/2.76 alpha15 [256, 2] (w:1, o:246, a:1, s:1, b:1),
% 2.36/2.76 alpha16 [257, 2] (w:1, o:247, a:1, s:1, b:1),
% 2.36/2.76 alpha17 [258, 2] (w:1, o:248, a:1, s:1, b:1),
% 2.36/2.76 alpha18 [259, 4] (w:1, o:310, a:1, s:1, b:1),
% 2.36/2.76 alpha19 [260, 3] (w:1, o:265, a:1, s:1, b:1),
% 2.36/2.76 alpha20 [261, 3] (w:1, o:269, a:1, s:1, b:1),
% 2.36/2.76 alpha21 [262, 4] (w:1, o:311, a:1, s:1, b:1),
% 2.36/2.76 alpha22 [263, 4] (w:1, o:312, a:1, s:1, b:1),
% 2.36/2.76 alpha23 [264, 3] (w:1, o:270, a:1, s:1, b:1),
% 2.36/2.76 alpha24 [265, 2] (w:1, o:235, a:1, s:1, b:1),
% 2.36/2.76 alpha25 [266, 2] (w:1, o:236, a:1, s:1, b:1),
% 2.36/2.76 alpha26 [267, 3] (w:1, o:271, a:1, s:1, b:1),
% 2.36/2.76 alpha27 [268, 3] (w:1, o:272, a:1, s:1, b:1),
% 2.36/2.76 alpha28 [269, 2] (w:1, o:237, a:1, s:1, b:1),
% 2.36/2.76 alpha29 [270, 3] (w:1, o:273, a:1, s:1, b:1),
% 2.36/2.76 alpha30 [271, 3] (w:1, o:274, a:1, s:1, b:1),
% 2.36/2.76 alpha31 [272, 3] (w:1, o:275, a:1, s:1, b:1),
% 2.36/2.76 alpha32 [273, 4] (w:1, o:313, a:1, s:1, b:1),
% 2.36/2.76 alpha33 [274, 4] (w:1, o:314, a:1, s:1, b:1),
% 14.34/14.77 alpha34 [275, 3] (w:1, o:276, a:1, s:1, b:1),
% 14.34/14.77 alpha35 [276, 2] (w:1, o:239, a:1, s:1, b:1),
% 14.34/14.77 alpha36 [277, 3] (w:1, o:277, a:1, s:1, b:1),
% 14.34/14.77 alpha37 [278, 3] (w:1, o:278, a:1, s:1, b:1),
% 14.34/14.77 alpha38 [279, 4] (w:1, o:315, a:1, s:1, b:1),
% 14.34/14.77 alpha39 [280, 3] (w:1, o:279, a:1, s:1, b:1),
% 14.34/14.77 alpha40 [281, 3] (w:1, o:280, a:1, s:1, b:1),
% 14.34/14.77 alpha41 [282, 4] (w:1, o:316, a:1, s:1, b:1),
% 14.34/14.77 alpha42 [283, 3] (w:1, o:281, a:1, s:1, b:1),
% 14.34/14.77 alpha43 [284, 3] (w:1, o:282, a:1, s:1, b:1),
% 14.34/14.77 alpha44 [285, 3] (w:1, o:283, a:1, s:1, b:1),
% 14.34/14.77 alpha45 [286, 4] (w:1, o:317, a:1, s:1, b:1),
% 14.34/14.77 alpha46 [287, 4] (w:1, o:318, a:1, s:1, b:1),
% 14.34/14.77 alpha47 [288, 3] (w:1, o:284, a:1, s:1, b:1),
% 14.34/14.77 alpha48 [289, 3] (w:1, o:285, a:1, s:1, b:1),
% 14.34/14.77 alpha49 [290, 2] (w:1, o:241, a:1, s:1, b:1),
% 14.34/14.77 alpha50 [291, 3] (w:1, o:286, a:1, s:1, b:1),
% 14.34/14.77 alpha51 [292, 4] (w:1, o:305, a:1, s:1, b:1),
% 14.34/14.77 alpha52 [293, 4] (w:1, o:306, a:1, s:1, b:1),
% 14.34/14.77 alpha53 [294, 4] (w:1, o:307, a:1, s:1, b:1),
% 14.34/14.77 skol1 [295, 2] (w:1, o:220, a:1, s:1, b:1),
% 14.34/14.77 skol2 [296, 2] (w:1, o:226, a:1, s:1, b:1),
% 14.34/14.77 skol3 [297, 2] (w:1, o:228, a:1, s:1, b:1),
% 14.34/14.77 skol4 [298, 1] (w:1, o:114, a:1, s:1, b:1),
% 14.34/14.77 skol5 [299, 3] (w:1, o:287, a:1, s:1, b:1),
% 14.34/14.77 skol6 [300, 3] (w:1, o:288, a:1, s:1, b:1),
% 14.34/14.77 skol7 [301, 3] (w:1, o:289, a:1, s:1, b:1),
% 14.34/14.77 skol8 [302, 3] (w:1, o:290, a:1, s:1, b:1),
% 14.34/14.77 skol9 [303, 3] (w:1, o:291, a:1, s:1, b:1),
% 14.34/14.77 skol10 [304, 2] (w:1, o:221, a:1, s:1, b:1),
% 14.34/14.77 skol11 [305, 2] (w:1, o:222, a:1, s:1, b:1),
% 14.34/14.77 skol12 [306, 4] (w:1, o:319, a:1, s:1, b:1),
% 14.34/14.77 skol13 [307, 2] (w:1, o:223, a:1, s:1, b:1),
% 14.34/14.77 skol14 [308, 2] (w:1, o:224, a:1, s:1, b:1),
% 14.34/14.77 skol15 [309, 2] (w:1, o:225, a:1, s:1, b:1),
% 14.34/14.77 skol16 [310, 3] (w:1, o:292, a:1, s:1, b:1),
% 14.34/14.77 skol17 [311, 3] (w:1, o:293, a:1, s:1, b:1),
% 14.34/14.77 skol18 [312, 3] (w:1, o:294, a:1, s:1, b:1),
% 14.34/14.77 skol19 [313, 3] (w:1, o:295, a:1, s:1, b:1),
% 14.34/14.77 skol20 [314, 3] (w:1, o:296, a:1, s:1, b:1),
% 14.34/14.77 skol21 [315, 3] (w:1, o:297, a:1, s:1, b:1),
% 14.34/14.77 skol22 [316, 3] (w:1, o:298, a:1, s:1, b:1),
% 14.34/14.77 skol23 [317, 4] (w:1, o:320, a:1, s:1, b:1),
% 14.34/14.77 skol24 [318, 3] (w:1, o:299, a:1, s:1, b:1),
% 14.34/14.77 skol25 [319, 2] (w:1, o:227, a:1, s:1, b:1),
% 14.34/14.77 skol26 [320, 3] (w:1, o:300, a:1, s:1, b:1),
% 14.34/14.77 skol27 [321, 3] (w:1, o:301, a:1, s:1, b:1),
% 14.34/14.77 skol28 [322, 3] (w:1, o:302, a:1, s:1, b:1).
% 14.34/14.77
% 14.34/14.77
% 14.34/14.77 Starting Search:
% 14.34/14.77
% 14.34/14.77 *** allocated 113905 integers for clauses
% 14.34/14.77 *** allocated 170857 integers for clauses
% 14.34/14.77 Resimplifying inuse:
% 14.34/14.77 Done
% 14.34/14.77
% 14.34/14.77
% 14.34/14.77 Intermediate Status:
% 14.34/14.77 Generated: 2939
% 14.34/14.77 Kept: 2007
% 14.34/14.77 Inuse: 35
% 14.34/14.77 Deleted: 1
% 14.34/14.77 Deletedinuse: 0
% 14.34/14.77
% 14.34/14.77 *** allocated 256285 integers for clauses
% 14.34/14.77 *** allocated 170857 integers for termspace/termends
% 14.34/14.77 Resimplifying inuse:
% 14.34/14.77 Done
% 14.34/14.77
% 14.34/14.77 Resimplifying inuse:
% 14.34/14.77 Done
% 14.34/14.77
% 14.34/14.77
% 14.34/14.77 Intermediate Status:
% 14.34/14.77 Generated: 6826
% 14.34/14.77 Kept: 4012
% 14.34/14.77 Inuse: 172
% 14.34/14.77 Deleted: 3
% 14.34/14.77 Deletedinuse: 1
% 14.34/14.77
% 14.34/14.77 *** allocated 384427 integers for clauses
% 14.34/14.77 *** allocated 256285 integers for termspace/termends
% 14.34/14.77 Resimplifying inuse:
% 14.34/14.77 Done
% 14.34/14.77
% 14.34/14.77 Resimplifying inuse:
% 14.34/14.77 Done
% 14.34/14.77
% 14.34/14.77
% 14.34/14.77 Intermediate Status:
% 14.34/14.77 Generated: 10848
% 14.34/14.77 Kept: 6109
% 14.34/14.77 Inuse: 229
% 14.34/14.77 Deleted: 3
% 14.34/14.77 Deletedinuse: 1
% 14.34/14.77
% 14.34/14.77 *** allocated 576640 integers for clauses
% 14.34/14.77 *** allocated 384427 integers for termspace/termends
% 14.34/14.77 Resimplifying inuse:
% 14.34/14.77 Done
% 14.34/14.77
% 14.34/14.77
% 14.34/14.77 Intermediate Status:
% 14.34/14.77 Generated: 20405
% 14.34/14.77 Kept: 8847
% 14.34/14.77 Inuse: 281
% 14.34/14.77 Deleted: 6
% 14.34/14.77 Deletedinuse: 1
% 14.34/14.77
% 14.34/14.77 Resimplifying inuse:
% 14.34/14.77 Done
% 14.34/14.77
% 14.34/14.77 Resimplifying inuse:
% 14.34/14.77 Done
% 14.34/14.77
% 14.34/14.77
% 14.34/14.77 Intermediate Status:
% 14.34/14.77 Generated: 27890
% 14.34/14.77 Kept: 10863
% 14.34/14.77 Inuse: 328
% 14.34/14.77 Deleted: 6
% 14.34/14.77 Deletedinuse: 1
% 14.34/14.77
% 14.34/14.77 Resimplifying inuse:
% 14.34/14.77 Done
% 14.34/14.77
% 14.34/14.77 *** allocated 576640 integers for termspace/termends
% 14.34/14.77 *** allocated 864960 integers for clauses
% 14.34/14.77 Resimplifying inuse:
% 14.34/14.77 Done
% 14.34/14.77
% 14.34/14.77
% 14.34/14.77 Intermediate Status:
% 14.34/14.77 Generated: 37776
% 14.34/14.77 Kept: 12981
% 14.34/14.77 Inuse: 346
% 14.34/14.77 Deleted: 6
% 14.34/14.77 Deletedinuse: 1
% 14.34/14.77
% 14.34/14.77 Resimplifying inuse:
% 14.34/14.77 Done
% 14.34/14.77
% 14.34/14.77 Resimplifying inuse:
% 14.34/14.77 Done
% 14.34/14.77
% 14.34/14.77
% 14.34/14.77 Intermediate Status:
% 14.34/14.77 Generated: 43514
% 14.34/14.77 Kept: 14995
% 14.34/14.77 Inuse: 394
% 14.34/14.77 Deleted: 7
% 14.34/14.77 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88
% 66.47/66.88 Intermediate Status:
% 66.47/66.88 Generated: 50200
% 66.47/66.88 Kept: 17438
% 66.47/66.88 Inuse: 415
% 66.47/66.88 Deleted: 7
% 66.47/66.88 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 *** allocated 1297440 integers for clauses
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 *** allocated 864960 integers for termspace/termends
% 66.47/66.88
% 66.47/66.88 Intermediate Status:
% 66.47/66.88 Generated: 56159
% 66.47/66.88 Kept: 19452
% 66.47/66.88 Inuse: 452
% 66.47/66.88 Deleted: 8
% 66.47/66.88 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 Resimplifying clauses:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88
% 66.47/66.88 Intermediate Status:
% 66.47/66.88 Generated: 60621
% 66.47/66.88 Kept: 21487
% 66.47/66.88 Inuse: 479
% 66.47/66.88 Deleted: 186
% 66.47/66.88 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88
% 66.47/66.88 Intermediate Status:
% 66.47/66.88 Generated: 66807
% 66.47/66.88 Kept: 24256
% 66.47/66.88 Inuse: 499
% 66.47/66.88 Deleted: 186
% 66.47/66.88 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88
% 66.47/66.88 Intermediate Status:
% 66.47/66.88 Generated: 72991
% 66.47/66.88 Kept: 26270
% 66.47/66.88 Inuse: 516
% 66.47/66.88 Deleted: 186
% 66.47/66.88 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 *** allocated 1946160 integers for clauses
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88
% 66.47/66.88 Intermediate Status:
% 66.47/66.88 Generated: 78144
% 66.47/66.88 Kept: 28423
% 66.47/66.88 Inuse: 544
% 66.47/66.88 Deleted: 186
% 66.47/66.88 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 *** allocated 1297440 integers for termspace/termends
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88
% 66.47/66.88 Intermediate Status:
% 66.47/66.88 Generated: 84525
% 66.47/66.88 Kept: 30470
% 66.47/66.88 Inuse: 569
% 66.47/66.88 Deleted: 186
% 66.47/66.88 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88
% 66.47/66.88 Intermediate Status:
% 66.47/66.88 Generated: 92921
% 66.47/66.88 Kept: 32507
% 66.47/66.88 Inuse: 579
% 66.47/66.88 Deleted: 186
% 66.47/66.88 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88
% 66.47/66.88 Intermediate Status:
% 66.47/66.88 Generated: 99822
% 66.47/66.88 Kept: 34509
% 66.47/66.88 Inuse: 597
% 66.47/66.88 Deleted: 186
% 66.47/66.88 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88
% 66.47/66.88 Intermediate Status:
% 66.47/66.88 Generated: 109797
% 66.47/66.88 Kept: 36534
% 66.47/66.88 Inuse: 616
% 66.47/66.88 Deleted: 186
% 66.47/66.88 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88
% 66.47/66.88 Intermediate Status:
% 66.47/66.88 Generated: 120122
% 66.47/66.88 Kept: 39490
% 66.47/66.88 Inuse: 634
% 66.47/66.88 Deleted: 186
% 66.47/66.88 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 Resimplifying clauses:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 *** allocated 1946160 integers for termspace/termends
% 66.47/66.88 *** allocated 2919240 integers for clauses
% 66.47/66.88
% 66.47/66.88 Intermediate Status:
% 66.47/66.88 Generated: 128935
% 66.47/66.88 Kept: 41663
% 66.47/66.88 Inuse: 679
% 66.47/66.88 Deleted: 324
% 66.47/66.88 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88
% 66.47/66.88 Intermediate Status:
% 66.47/66.88 Generated: 134908
% 66.47/66.88 Kept: 43667
% 66.47/66.88 Inuse: 711
% 66.47/66.88 Deleted: 324
% 66.47/66.88 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88
% 66.47/66.88 Intermediate Status:
% 66.47/66.88 Generated: 142766
% 66.47/66.88 Kept: 45678
% 66.47/66.88 Inuse: 739
% 66.47/66.88 Deleted: 324
% 66.47/66.88 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88
% 66.47/66.88 Intermediate Status:
% 66.47/66.88 Generated: 152154
% 66.47/66.88 Kept: 47920
% 66.47/66.88 Inuse: 769
% 66.47/66.88 Deleted: 324
% 66.47/66.88 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88
% 66.47/66.88 Intermediate Status:
% 66.47/66.88 Generated: 159167
% 66.47/66.88 Kept: 50034
% 66.47/66.88 Inuse: 824
% 66.47/66.88 Deleted: 324
% 66.47/66.88 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88
% 66.47/66.88 Intermediate Status:
% 66.47/66.88 Generated: 165834
% 66.47/66.88 Kept: 52130
% 66.47/66.88 Inuse: 879
% 66.47/66.88 Deleted: 324
% 66.47/66.88 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88
% 66.47/66.88 Intermediate Status:
% 66.47/66.88 Generated: 174422
% 66.47/66.88 Kept: 54131
% 66.47/66.88 Inuse: 922
% 66.47/66.88 Deleted: 324
% 66.47/66.88 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88
% 66.47/66.88 Intermediate Status:
% 66.47/66.88 Generated: 183608
% 66.47/66.88 Kept: 56144
% 66.47/66.88 Inuse: 952
% 66.47/66.88 Deleted: 324
% 66.47/66.88 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88
% 66.47/66.88 Intermediate Status:
% 66.47/66.88 Generated: 190743
% 66.47/66.88 Kept: 58255
% 66.47/66.88 Inuse: 964
% 66.47/66.88 Deleted: 324
% 66.47/66.88 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 *** allocated 2919240 integers for termspace/termends
% 66.47/66.88
% 66.47/66.88 Intermediate Status:
% 66.47/66.88 Generated: 200730
% 66.47/66.88 Kept: 60529
% 66.47/66.88 Inuse: 979
% 66.47/66.88 Deleted: 324
% 66.47/66.88 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 Resimplifying clauses:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 *** allocated 4378860 integers for clauses
% 66.47/66.88
% 66.47/66.88 Intermediate Status:
% 66.47/66.88 Generated: 225538
% 66.47/66.88 Kept: 64843
% 66.47/66.88 Inuse: 989
% 66.47/66.88 Deleted: 659
% 66.47/66.88 Deletedinuse: 1
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 66.47/66.88 Done
% 66.47/66.88
% 66.47/66.88 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 240076
% 234.59/235.00 Kept: 67331
% 234.59/235.00 Inuse: 1014
% 234.59/235.00 Deleted: 659
% 234.59/235.00 Deletedinuse: 1
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 248540
% 234.59/235.00 Kept: 69445
% 234.59/235.00 Inuse: 1015
% 234.59/235.00 Deleted: 661
% 234.59/235.00 Deletedinuse: 3
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 257145
% 234.59/235.00 Kept: 73086
% 234.59/235.00 Inuse: 1019
% 234.59/235.00 Deleted: 661
% 234.59/235.00 Deletedinuse: 3
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 268136
% 234.59/235.00 Kept: 77684
% 234.59/235.00 Inuse: 1044
% 234.59/235.00 Deleted: 661
% 234.59/235.00 Deletedinuse: 3
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 282854
% 234.59/235.00 Kept: 81166
% 234.59/235.00 Inuse: 1074
% 234.59/235.00 Deleted: 661
% 234.59/235.00 Deletedinuse: 3
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00 Resimplifying clauses:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 291956
% 234.59/235.00 Kept: 86467
% 234.59/235.00 Inuse: 1084
% 234.59/235.00 Deleted: 5151
% 234.59/235.00 Deletedinuse: 3
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 306155
% 234.59/235.00 Kept: 90289
% 234.59/235.00 Inuse: 1119
% 234.59/235.00 Deleted: 5151
% 234.59/235.00 Deletedinuse: 3
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 311138
% 234.59/235.00 Kept: 93458
% 234.59/235.00 Inuse: 1124
% 234.59/235.00 Deleted: 5151
% 234.59/235.00 Deletedinuse: 3
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00 *** allocated 4378860 integers for termspace/termends
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 323676
% 234.59/235.00 Kept: 98981
% 234.59/235.00 Inuse: 1149
% 234.59/235.00 Deleted: 5151
% 234.59/235.00 Deletedinuse: 3
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00 *** allocated 6568290 integers for clauses
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 329571
% 234.59/235.00 Kept: 101211
% 234.59/235.00 Inuse: 1159
% 234.59/235.00 Deleted: 5151
% 234.59/235.00 Deletedinuse: 3
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00 Resimplifying clauses:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 343521
% 234.59/235.00 Kept: 107523
% 234.59/235.00 Inuse: 1194
% 234.59/235.00 Deleted: 5229
% 234.59/235.00 Deletedinuse: 3
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 349926
% 234.59/235.00 Kept: 109543
% 234.59/235.00 Inuse: 1229
% 234.59/235.00 Deleted: 5229
% 234.59/235.00 Deletedinuse: 3
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 362419
% 234.59/235.00 Kept: 114013
% 234.59/235.00 Inuse: 1244
% 234.59/235.00 Deleted: 5230
% 234.59/235.00 Deletedinuse: 4
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 369819
% 234.59/235.00 Kept: 117252
% 234.59/235.00 Inuse: 1274
% 234.59/235.00 Deleted: 5230
% 234.59/235.00 Deletedinuse: 4
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 385551
% 234.59/235.00 Kept: 123679
% 234.59/235.00 Inuse: 1304
% 234.59/235.00 Deleted: 5230
% 234.59/235.00 Deletedinuse: 4
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00 Resimplifying clauses:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 394437
% 234.59/235.00 Kept: 125930
% 234.59/235.00 Inuse: 1334
% 234.59/235.00 Deleted: 5493
% 234.59/235.00 Deletedinuse: 5
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 401618
% 234.59/235.00 Kept: 127937
% 234.59/235.00 Inuse: 1352
% 234.59/235.00 Deleted: 5495
% 234.59/235.00 Deletedinuse: 6
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 409487
% 234.59/235.00 Kept: 130093
% 234.59/235.00 Inuse: 1368
% 234.59/235.00 Deleted: 5495
% 234.59/235.00 Deletedinuse: 6
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 415758
% 234.59/235.00 Kept: 132099
% 234.59/235.00 Inuse: 1402
% 234.59/235.00 Deleted: 5495
% 234.59/235.00 Deletedinuse: 6
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 422306
% 234.59/235.00 Kept: 134168
% 234.59/235.00 Inuse: 1448
% 234.59/235.00 Deleted: 5495
% 234.59/235.00 Deletedinuse: 6
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 430344
% 234.59/235.00 Kept: 136394
% 234.59/235.00 Inuse: 1483
% 234.59/235.00 Deleted: 5495
% 234.59/235.00 Deletedinuse: 6
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 439094
% 234.59/235.00 Kept: 138673
% 234.59/235.00 Inuse: 1508
% 234.59/235.00 Deleted: 5495
% 234.59/235.00 Deletedinuse: 6
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 447725
% 234.59/235.00 Kept: 140695
% 234.59/235.00 Inuse: 1529
% 234.59/235.00 Deleted: 5495
% 234.59/235.00 Deletedinuse: 6
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00
% 234.59/235.00 Intermediate Status:
% 234.59/235.00 Generated: 455455
% 234.59/235.00 Kept: 142704
% 234.59/235.00 Inuse: 1560
% 234.59/235.00 Deleted: 5495
% 234.59/235.00 Deletedinuse: 6
% 234.59/235.00
% 234.59/235.00 Resimplifying inuse:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00 Resimplifying clauses:
% 234.59/235.00 Done
% 234.59/235.00
% 234.59/235.00 ResimplCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------