TSTP Solution File: SWW240+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW240+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.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 23:21:29 EDT 2022
% Result : Timeout 300.04s 300.48s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW240+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Sat Jun 4 09:57:47 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.99/1.59 *** allocated 10000 integers for termspace/termends
% 0.99/1.59 *** allocated 10000 integers for clauses
% 0.99/1.59 *** allocated 10000 integers for justifications
% 0.99/1.59 *** allocated 15000 integers for termspace/termends
% 0.99/1.59 *** allocated 22500 integers for termspace/termends
% 0.99/1.59 *** allocated 33750 integers for termspace/termends
% 0.99/1.59 Bliksem 1.12
% 0.99/1.59
% 0.99/1.59
% 0.99/1.59 Automatic Strategy Selection
% 0.99/1.59
% 0.99/1.59 *** allocated 50625 integers for termspace/termends
% 0.99/1.59 *** allocated 75937 integers for termspace/termends
% 0.99/1.59 *** allocated 113905 integers for termspace/termends
% 0.99/1.59
% 0.99/1.59 Clauses:
% 0.99/1.59
% 0.99/1.59 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.59 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.99/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.99/1.59 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.99/1.59 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.99/1.59 ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.99/1.59 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.99/1.59 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.99/1.59 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.99/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.59 = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.59 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.59 = Y }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.59 = Y }.
% 0.99/1.59 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.59 = Y }.
% 0.99/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.99/1.59 = Y }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.99/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_Nat_Onat ) ) = Y }.
% 0.99/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_Nat_Onat ) ) = Y }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.59 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.99/1.59 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.99/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.59 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.99/1.59 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.99/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.99/1.59 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.99/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.99/1.59 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.99/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.99/1.59 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.99/1.59 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.99/1.59 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.99/1.59 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.99/1.59 = Y }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.99/1.59 = Y }.
% 0.99/1.59 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.99/1.59 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.99/1.59 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.99/1.59 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.99/1.59 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 0.99/1.59 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.99/1.59 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.99/1.59 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.59 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.59 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.59 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.99/1.59 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.99/1.59 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.59 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.99/1.59 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.99/1.59 .
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.59 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.99/1.59 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.99/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.99/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.99/1.59 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.99/1.59 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.99/1.59 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.99/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.99/1.59 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.99/1.59 = Y }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.99/1.59 ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.99/1.59 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.99/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.99/1.59 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.99/1.59 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.99/1.59 ), X ) ) }.
% 0.99/1.59 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.59 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.99/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.59 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.99/1.59 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 X ) }.
% 0.99/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( X ) }.
% 0.99/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.59 , Y ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.59 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.59 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.59 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.59 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.59 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.99/1.59 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.99/1.59 ( X, Y ) }.
% 0.99/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.59 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.59 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.99/1.59 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.99/1.59 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.99/1.59 Y ) ) = Y }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.99/1.59 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.99/1.59 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.99/1.59 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.99/1.59 ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.99/1.59 ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.99/1.59 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.59 , Y ) }.
% 0.99/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.99/1.59 , Y ) }.
% 0.99/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.99/1.59 = Y }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.99/1.59 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.99/1.59 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.99/1.59 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.99/1.59 ( X, Y ), Z ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.99/1.59 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.99/1.59 ( X, Z ), Y ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.99/1.59 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.99/1.59 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.99/1.59 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.99/1.59 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 Z, Y ) ) = Y }.
% 0.99/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.99/1.59 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.99/1.59 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.99/1.59 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.99/1.59 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.99/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 T, Y ), Z = Y }.
% 0.99/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 T, Y ) }.
% 0.99/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 Y, Z ), T = Y }.
% 0.99/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 Y, Z ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.99/1.59 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, T, Y ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.59 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.59 , Y, Z ) ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.99/1.59 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, Z, Y ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.59 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.59 , T, Y ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.99/1.59 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.99/1.59 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.99/1.59 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.99/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.99/1.59 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.99/1.59 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.99/1.59 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.59 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.99/1.59 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.59 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.59 , Y, T ) ) }.
% 0.99/1.59 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.59 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.59 , T, Y ) ) }.
% 0.99/1.59 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.59 , T ) ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.99/1.59 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.59 Z ) = Y }.
% 0.99/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 T, Y ), Z = Y }.
% 0.99/1.59 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 T, Y ), Z = Y }.
% 0.99/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 Y, T ), Z = Y }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.99/1.59 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, Z, Y ) }.
% 0.99/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.99/1.59 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, Z, Y ) }.
% 0.99/1.59 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.99/1.59 ( X, Y ), Z = Y }.
% 0.99/1.59 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.99/1.59 ( X, Y ) }.
% 0.99/1.59 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.59 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.99/1.59 ) ) }.
% 0.99/1.59 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.99/1.59 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.99/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.59 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.99/1.59 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.99/1.59 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.99/1.59 .
% 0.99/1.59 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.99/1.59 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.99/1.59 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ) }.
% 0.99/1.59 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.99/1.59 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.99/1.59 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.99/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.99/1.59 ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.99/1.59 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.99/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.99/1.59 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.99/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.99/1.59 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.99/1.59 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.59 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.99/1.59 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.99/1.59 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.99/1.59 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.59 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.59 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.59 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.99/1.59 ) }.
% 0.99/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.59 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.99/1.59 ), ! U = T }.
% 0.99/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.59 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.99/1.59 ), ! Z = Y }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.99/1.59 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.99/1.59 ) ), Z ) }.
% 0.99/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.59 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.99/1.59 ), U = Z, T = Y }.
% 0.99/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.59 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.99/1.59 ) }.
% 0.99/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.59 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.99/1.59 ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.99/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( X ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.99/1.59 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.99/1.59 ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.59 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.59 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.99/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.99/1.59 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.99/1.59 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.59 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.99/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.59 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Z, Y ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.59 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.99/1.59 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.99/1.59 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.99/1.59 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.99/1.59 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.99/1.59 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.99/1.59 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.59 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.99/1.59 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.59 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.99/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.99/1.59 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.99/1.59 ( X, Z ) }.
% 0.99/1.59 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.59 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.99/1.59 ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.99/1.59 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.99/1.59 .
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.99/1.59 .
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.99/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.99/1.59 { alpha55( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.99/1.59 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.99/1.59 { alpha55( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.99/1.59 ( X, Y ), Z ) ) }.
% 0.99/1.59 { ! alpha55( X, Y, Z ), alpha58( X, Y, Z ), Z = Y }.
% 0.99/1.59 { ! alpha55( X, Y, Z ), alpha58( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.99/1.59 ) ) }.
% 0.99/1.59 { ! alpha58( X, Y, Z ), alpha55( X, Y, Z ) }.
% 0.99/1.59 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha55( X, Y, Z ) }.
% 0.99/1.59 { ! alpha58( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.99/1.59 }.
% 0.99/1.59 { ! alpha58( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.99/1.59 X, Y ), Z ) ), alpha58( X, Y, Z ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.99/1.59 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.99/1.59 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.99/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.99/1.59 ) ) }.
% 0.99/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.99/1.59 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.99/1.59 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.99/1.59 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.99/1.59 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.99/1.59 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.59 X, Y, Z ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.99/1.59 .
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.99/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.99/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.99/1.59 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.99/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.99/1.59 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.99/1.59 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.99/1.59 .
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.99/1.59 .
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.99/1.59 .
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.99/1.59 , X ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.99/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.99/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.99/1.59 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.99/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.59 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.99/1.59 ) ), T ), Y ) }.
% 0.99/1.59 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.99/1.59 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.99/1.59 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.99/1.59 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.99/1.59 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.99/1.59 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.99/1.59 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.99/1.59 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.99/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.99/1.59 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.99/1.59 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.99/1.59 ( X, Y ) ) }.
% 0.99/1.59 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.99/1.59 ) ), Y ) }.
% 0.99/1.59 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.99/1.59 ( X, Y ) ) }.
% 0.99/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), X ) = X }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ) ) = X }.
% 0.99/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.99/1.59 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.99/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.99/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.99/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.99/1.59 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.99/1.59 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.99/1.59 .
% 0.99/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.99/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.99/1.59 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.99/1.59 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.99/1.59 .
% 0.99/1.59 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.99/1.59 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), Z ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.99/1.59 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.99/1.59 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.99/1.59 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 Y ), X ) ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_Nat_Onat ) }.
% 0.99/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_Nat_Onat ) }.
% 0.99/1.59 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.99/1.59 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.59 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.59 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.99/1.59 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.99/1.59 , Y ), X ) }.
% 0.99/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.59 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.99/1.59 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( X ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.99/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.99/1.59 .
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.99/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.99/1.59 .
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.59 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( X ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.59 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( X ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.99/1.59 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.59 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.99/1.59 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha1( X, Y, Z, T ),
% 0.99/1.59 alpha20( X, Y, Z, T ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z, T ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha20( X, Y, Z, T ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.59 { ! alpha20( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! alpha20( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.59 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha20( X, Y, Z, T ) }.
% 0.99/1.59 { ! alpha1( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.99/1.59 { ! alpha1( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.99/1.59 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha1( X, Y, Z, T ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha2( X, Y, Z, T ),
% 0.99/1.59 alpha21( X, Y, Z, T ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z, T ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha21( X, Y, Z, T ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.59 { ! alpha21( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! alpha21( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.59 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha21( X, Y, Z, T ) }.
% 0.99/1.59 { ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.99/1.59 { ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.99/1.59 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha2( X, Y, Z, T ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.59 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.99/1.59 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.99/1.59 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.99/1.59 ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.99/1.59 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.99/1.59 ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.59 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.99/1.59 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), Y ) }.
% 0.99/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.99/1.59 ), X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.99/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.99/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.99/1.59 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.59 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.59 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.59 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.59 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.59 tc_Nat_Onat ), X ), Y ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.59 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.99/1.59 ) ) }.
% 0.99/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.99/1.59 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.59 ) ) }.
% 0.99/1.59 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.59 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.99/1.59 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.99/1.59 { ! class_Groups_Ozero( X ), !
% 0.99/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.59 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.59 tc_Polynomial_Opoly( X ) ),
% 0.99/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.59 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.59 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.99/1.59 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.59 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.59 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.99/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.99/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.99/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.99/1.59 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.99/1.59 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.99/1.59 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.99/1.59 .
% 0.99/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.99/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.99/1.59 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.99/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.99/1.60 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.99/1.60 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.99/1.60 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.60 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.60 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.99/1.60 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.60 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.60 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.99/1.60 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.99/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.99/1.60 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.99/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.99/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.99/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.99/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.99/1.60 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.60 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.99/1.60 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.60 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.99/1.60 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.99/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.60 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.99/1.60 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.99/1.60 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.60 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.99/1.60 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.99/1.60 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.99/1.60 .
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.60 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.99/1.60 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.60 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.60 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.60 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.60 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.60 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.60 c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.99/1.60 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.99/1.60 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.99/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.99/1.60 ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.99/1.60 ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, Z, X ), Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.99/1.60 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, Z, Y ), X ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.99/1.60 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.99/1.60 .
% 0.99/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.99/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.99/1.60 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.99/1.60 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.99/1.60 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.99/1.60 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.99/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.99/1.60 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 0.99/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.99/1.60 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.99/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.99/1.60 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.99/1.60 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.99/1.60 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.99/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.99/1.60 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.99/1.60 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.99/1.60 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.99/1.60 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.99/1.60 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.60 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.60 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.99/1.60 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.99/1.60 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.99/1.60 hAPP( Z, Y ) ) }.
% 0.99/1.60 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.60 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.99/1.60 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.99/1.60 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.99/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Int_Oint ), X ) = X }.
% 0.99/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Int_Oint ) ) = X }.
% 0.99/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.99/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.99/1.60 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.99/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.99/1.60 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.99/1.60 .
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.99/1.60 .
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.99/1.60 tc_Int_Oint ) ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.99/1.60 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.99/1.60 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.99/1.60 }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.99/1.60 tc_Int_Oint ) ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.99/1.60 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.99/1.60 = X }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.99/1.60 tc_Int_Oint ) ) ) }.
% 0.99/1.60 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.99/1.60 tc_Int_Oint ) ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.99/1.60 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.99/1.60 }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.99/1.60 tc_Int_Oint ) ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Int_Oint ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.99/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.99/1.60 c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) = c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Int_Oint ) }.
% 0.99/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.99/1.60 tc_Int_Oint ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.99/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.60 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.99/1.60 ( tc_Int_Oint ) }.
% 0.99/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.60 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.60 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.99/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.60 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.60 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.60 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.99/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.60 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.60 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.99/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.99/1.60 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.60 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.99/1.60 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.99/1.60 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.99/1.60 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.99/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.99/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.99/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.60 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.99/1.60 ) }.
% 0.99/1.60 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.99/1.60 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.99/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.99/1.60 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.99/1.60 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.99/1.60 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.60 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.60 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.99/1.60 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.99/1.60 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.99/1.60 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.99/1.60 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.99/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.99/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.99/1.60 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.99/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.99/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.60 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.60 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.60 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.60 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.99/1.60 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.60 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.99/1.60 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.99/1.60 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.60 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.99/1.60 ) }.
% 0.99/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.99/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.99/1.60 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.99/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.99/1.60 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.99/1.60 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.60 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.60 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.60 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.60 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.60 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.99/1.60 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.60 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.99/1.60 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.60 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.60 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.60 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol2( X, Y ) ) }.
% 0.99/1.60 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.99/1.60 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.99/1.60 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.60 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.99/1.60 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.99/1.60 ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.60 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.99/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.99/1.60 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.99/1.60 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.60 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.60 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.99/1.60 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.99/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.99/1.60 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.99/1.60 .
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.99/1.60 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.99/1.60 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.99/1.60 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.99/1.60 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.99/1.60 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.60 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( X ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.99/1.60 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.99/1.60 , Z, Y ) }.
% 0.99/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.60 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.99/1.60 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.60 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.99/1.60 Z ) ), Y ) ) }.
% 0.99/1.60 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.60 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.60 W ) ), U ), Y ) }.
% 0.99/1.60 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.99/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.99/1.60 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.60 ( X ), Z ), U ), Y ) }.
% 0.99/1.60 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.60 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.99/1.60 Z ) ), U ), T ) = Y }.
% 0.99/1.60 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.99/1.60 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.60 ( X ), Z ), U ), Y ) }.
% 0.99/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.99/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.99/1.60 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.99/1.60 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.99/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.99/1.60 X, Y ) }.
% 0.99/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.99/1.60 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.60 , Y ) ) }.
% 0.99/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.99/1.60 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.99/1.60 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.99/1.60 X, Y ) ) }.
% 0.99/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.99/1.60 X, Z, Y ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.60 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha3( X, Y
% 0.99/1.60 , Z ), alpha22( X, Y, Z ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha22( X, Y, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.60 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.60 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.99/1.60 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ), alpha22( X, Y, Z ) }.
% 0.99/1.60 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.99/1.60 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), alpha3( X, Y, Z ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( X ) ), alpha4( X, Y, Z ), alpha23( X, Y, Z ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha23( X, Y, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( X ) ) }.
% 0.99/1.60 { ! alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.60 { ! alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.99/1.60 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( X ), Y ), alpha23( X, Y, Z ) }.
% 0.99/1.60 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.99/1.60 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ), alpha4( X, Y, Z ) }.
% 0.99/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( X ) ) }.
% 0.99/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.60 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.60 { ! class_Rings_Oordered__semiring( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.60 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.60 { ! class_Rings_Oordered__semiring( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.60 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.60 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.60 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.99/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.99/1.60 { ! class_Rings_Oordered__semiring( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.60 { ! class_Rings_Oordered__semiring( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.60 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.60 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( X ) ) }.
% 0.99/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ) }.
% 0.99/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.60 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.99/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.99/1.60 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 ) }.
% 0.99/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.99/1.60 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.99/1.60 ) }.
% 0.99/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.99/1.60 .
% 0.99/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.99/1.60 .
% 0.99/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.99/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.60 Y, Z ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.60 Z, Y ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.60 ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.99/1.60 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.99/1.60 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.99/1.60 , Y, T ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.60 c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.60 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.99/1.60 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.60 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.99/1.60 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.60 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ) }.
% 0.99/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.99/1.60 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.60 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.99/1.60 ( X, Y ), Y ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.60 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.60 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, Z, X ), Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.99/1.60 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.99/1.60 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.99/1.60 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.99/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.99/1.60 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.99/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.99/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.99/1.60 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.60 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.99/1.60 .
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.60 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.99/1.60 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.99/1.60 .
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.60 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.99/1.60 .
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.60 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.99/1.60 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.99/1.60 .
% 0.99/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.60 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.99/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( X, Z, W ) ), U ), Y ) ) }.
% 0.99/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.99/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.60 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.60 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.99/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.60 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.99/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.99/1.60 X, W, Z ) ), U ), T ), Y ) }.
% 0.99/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.60 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.99/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.60 ( X ), Z ), U ), Y ) ) }.
% 0.99/1.60 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.99/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.99/1.60 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.99/1.60 .
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.60 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.99/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.99/1.60 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.60 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.60 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.60 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.60 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.60 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.99/1.60 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.99/1.60 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.99/1.60 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.99/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.99/1.60 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.99/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.60 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.60 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.99/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.60 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.60 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.60 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.99/1.60 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.99/1.60 ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.99/1.60 ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.60 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.99/1.60 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.60 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.99/1.60 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.99/1.60 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.99/1.60 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.99/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.99/1.60 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.99/1.60 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.60 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.99/1.60 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.60 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.99/1.60 , alpha5( X, Y, Z ) }.
% 0.99/1.60 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.99/1.60 , alpha24( X, Y, Z ) }.
% 0.99/1.60 { ! alpha5( X, Y, Z ), ! alpha24( X, Y, Z ), hBOOL( hAPP( Z,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.99/1.60 { ! alpha24( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.99/1.60 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.99/1.60 { ! hBOOL( hAPP( Z, skol3( T, U, Z ) ) ), alpha24( X, Y, Z ) }.
% 0.99/1.60 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol3( X, Y, Z ) ),
% 0.99/1.60 alpha24( X, Y, Z ) }.
% 0.99/1.60 { ! alpha5( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.99/1.60 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha5( X, Y, Z ) }.
% 0.99/1.60 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha5
% 0.99/1.60 ( X, Y, Z ) }.
% 0.99/1.60 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.99/1.60 , ! alpha6( X, Y, Z ) }.
% 0.99/1.60 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.99/1.60 , ! alpha25( X, Y, Z ) }.
% 0.99/1.60 { alpha6( X, Y, Z ), alpha25( X, Y, Z ), hBOOL( hAPP( Z,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.99/1.60 { ! alpha25( X, Y, Z ), ! hBOOL( hAPP( Z, skol4( T, U, Z ) ) ) }.
% 0.99/1.60 { ! alpha25( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.99/1.60 skol4( X, Y, Z ) ) }.
% 0.99/1.60 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.99/1.60 ) ), alpha25( X, Y, Z ) }.
% 0.99/1.60 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 0.99/1.60 .
% 0.99/1.60 { ! alpha6( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ) ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha6( X, Y, Z ) }.
% 0.99/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 0.99/1.60 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.99/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.99/1.60 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.99/1.60 ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.99/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.99/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.99/1.60 ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.99/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.99/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.99/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.99/1.60 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.60 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.99/1.60 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.99/1.60 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.99/1.60 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.99/1.60 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.60 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.99/1.60 ), Y ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.99/1.60 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ), alpha7
% 0.99/1.60 ( X, Y, Z ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.99/1.60 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! alpha7( X, Y, Z ),
% 0.99/1.60 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.99/1.60 { ! alpha7( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 0.99/1.60 ( X ) ) }.
% 0.99/1.60 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.99/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.99/1.60 alpha7( X, Y, Z ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.99/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.99/1.60 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.99/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.60 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.99/1.60 ( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 0.99/1.60 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.60 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.99/1.60 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 0.99/1.60 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.99/1.60 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.99/1.60 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 0.99/1.60 ( X ) ) ) }.
% 0.99/1.60 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.99/1.60 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.99/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.60 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.60 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.99/1.60 ( tc_Int_Oint ), Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.99/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.99/1.60 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.99/1.60 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.99/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.99/1.60 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.99/1.60 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.99/1.60 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.99/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.60 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.60 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.99/1.60 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.99/1.60 .
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.99/1.60 ( tc_Int_Oint ) ) ) }.
% 0.99/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.99/1.60 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.99/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.99/1.60 tc_Polynomial_Opoly( X ), Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.99/1.60 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.99/1.60 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.60 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.99/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.99/1.60 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Int_Oint, X, Y ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.99/1.60 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.99/1.60 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.99/1.60 ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Int_Oint ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.99/1.60 tc_Int_Oint ) ) }.
% 0.99/1.60 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.99/1.60 , Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.99/1.60 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Int_Oint, X, Y ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.99/1.60 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.99/1.60 ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol5( X, Y ) ) }.
% 0.99/1.60 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.99/1.60 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.99/1.60 hAPP( Y, U ) ) }.
% 0.99/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.99/1.60 ( Z, skol6( X, Y, Z ) ), hAPP( Y, skol6( X, Y, Z ) ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.60 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.99/1.60 ( X, Z, Y ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.99/1.60 ( X, Y, Z ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.60 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.99/1.60 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.99/1.60 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.99/1.60 hAPP( Y, U ) ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.60 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.60 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.60 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.60 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.99/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.99/1.60 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.60 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.60 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.99/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.60 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.60 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.99/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.99/1.60 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.99/1.60 hAPP( Y, U ) ) }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.60 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.60 Y ) }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.99/1.60 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.60 Y ), ! Z = Y }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.60 Z ), ! Z = Y }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.60 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.60 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.60 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.60 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.60 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.99/1.60 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.60 , ! Z = Y }.
% 0.99/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.60 , ! Z = Y }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.60 , ! Y = Z }.
% 0.99/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.60 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.99/1.60 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.99/1.60 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.99/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.99/1.60 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.60 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.60 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.60 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 0.99/1.60 ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.99/1.60 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Int_Oint, X, Y ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.60 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.60 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.99/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.60 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.60 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.60 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.60 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.60 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.60 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.60 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.60 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.60 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.60 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.60 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.99/1.60 ( X, Z, Y ) }.
% 0.99/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.60 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.99/1.60 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.60 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.60 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.99/1.60 , ! Z = Y }.
% 0.99/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.60 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.99/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.99/1.60 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.99/1.60 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.99/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.60 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.99/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.99/1.60 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.99/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.99/1.60 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.99/1.60 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.99/1.60 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 0.99/1.60 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.99/1.60 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.99/1.60 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.99/1.60 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.99/1.60 .
% 0.99/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.99/1.60 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.99/1.60 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.99/1.60 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.99/1.60 ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.99/1.60 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.60 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.99/1.60 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.99/1.60 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.99/1.60 , Y ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.99/1.60 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.99/1.60 ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 0.99/1.60 , Z, Y ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.99/1.60 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 0.99/1.60 ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.99/1.60 ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.99/1.60 Z, T ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.99/1.60 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.99/1.60 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.99/1.60 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.99/1.60 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.99/1.60 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.99/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.99/1.60 ), T ), U ), Y ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.99/1.60 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 0.99/1.60 .
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.99/1.60 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 0.99/1.60 .
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.99/1.60 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.99/1.60 ( X ), Y ), Z ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.99/1.60 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.99/1.60 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.99/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.60 X ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.60 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 0.99/1.60 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.99/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.99/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.99/1.60 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.99/1.60 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 0.99/1.60 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.99/1.60 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.99/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.99/1.60 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.99/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.99/1.60 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.99/1.60 hAPP( Z, skol7( U, W, Z ) ) ) }.
% 0.99/1.60 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.99/1.60 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol7( X
% 0.99/1.60 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.60 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 0.99/1.60 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol28( X,
% 0.99/1.60 Y, Z ) ) ) ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 0.99/1.60 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.60 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.99/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 0.99/1.60 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 0.99/1.60 ) ) }.
% 0.99/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.99/1.60 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 0.99/1.60 .
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 0.99/1.60 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Int_Oint, Y, X ), X = Y }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.99/1.60 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Int_Oint, Y, X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.99/1.60 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 0.99/1.60 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.99/1.60 , Z ), X ) ), T ) ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Int_Oint, U, T ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.99/1.60 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.60 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.99/1.60 X ) ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X )
% 0.99/1.60 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y )
% 0.99/1.60 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.99/1.60 ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.99/1.60 ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.99/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.99/1.60 ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.99/1.60 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 0.99/1.60 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.99/1.60 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.99/1.60 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.99/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.99/1.60 Y ) ) ), Y ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.99/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.99/1.60 Y ) ) ), Y ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Nat_Onat, Z, X ) }.
% 0.99/1.60 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.99/1.60 X ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.99/1.60 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha8( X, Y ), Y = X }
% 0.99/1.60 .
% 0.99/1.60 { ! alpha8( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! alpha8( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! alpha8( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, X, Y ), alpha8( X, Y ) }.
% 0.99/1.60 { ! alpha9( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! alpha9( X, Y ), ! Y = X }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha9( X, Y ) }
% 0.99/1.60 .
% 0.99/1.60 { ! alpha9( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! alpha9( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, X, Y ), alpha9( X, Y ) }.
% 0.99/1.60 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.99/1.60 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, Y, X ), Y = X }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.99/1.60 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Nat_Onat, Y, Z ) }.
% 0.99/1.60 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Nat_Onat, Y, Z ) }.
% 0.99/1.60 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 0.99/1.60 , Z ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 0.99/1.60 Z, Y ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Nat_Onat, Y, Z ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.99/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.99/1.60 }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.99/1.60 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.99/1.60 X ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.99/1.60 .
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.99/1.60 .
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.99/1.60 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.99/1.60 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.99/1.60 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.99/1.60 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.99/1.60 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.99/1.60 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.99/1.60 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.99/1.60 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.60 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.99/1.60 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.60 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.60 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.99/1.60 { ! X = c_Nat_OSuc( X ) }.
% 0.99/1.60 { ! c_Nat_OSuc( X ) = X }.
% 0.99/1.60 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.99/1.60 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.99/1.60 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.99/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.99/1.60 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.99/1.60 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.99/1.60 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.99/1.60 ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.99/1.60 .
% 0.99/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.99/1.60 ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.99/1.60 , c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.99/1.60 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.99/1.60 }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.99/1.60 c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.99/1.60 ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.60 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.60 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.99/1.60 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.99/1.60 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha10( X, Y ) }.
% 0.99/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! alpha10( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.99/1.60 c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! alpha10( X, Y ), Y = c_Nat_OSuc( skol8( Z, Y ) ) }.
% 0.99/1.60 { ! alpha10( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol8( X,
% 0.99/1.60 Y ), X ) }.
% 0.99/1.60 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.99/1.60 ), alpha10( X, Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol9( X ) ) }.
% 0.99/1.60 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.99/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha11( X, Y ), alpha26( X
% 0.99/1.60 , Y ) }.
% 0.99/1.60 { ! alpha11( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.99/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! alpha26( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.99/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! alpha26( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { ! alpha26( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha26( X, Y ) }.
% 0.99/1.60 { ! alpha11( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! alpha11( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha11( X, Y ) }.
% 0.99/1.60 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha12( X, Y ),
% 0.99/1.60 alpha27( X, Y ) }.
% 0.99/1.60 { ! alpha12( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.60 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! alpha27( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.60 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! alpha27( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { ! alpha27( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha27( X, Y ) }.
% 0.99/1.60 { ! alpha12( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! alpha12( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.60 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha12( X, Y ) }.
% 0.99/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.99/1.60 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.99/1.60 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.99/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol10( X, Y ) ) ) }.
% 0.99/1.60 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.99/1.60 .
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.99/1.60 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.99/1.60 ), X ) ) }.
% 0.99/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.99/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.99/1.60 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.99/1.60 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.99/1.60 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.99/1.60 ), X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.99/1.60 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.99/1.60 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.99/1.60 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.99/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.60 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.99/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.99/1.60 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.99/1.60 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.99/1.60 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 X ), Y ), Z = Y }.
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.99/1.60 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.99/1.60 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.60 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.99/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.99/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.99/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.99/1.60 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.99/1.60 ) ) = X }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.60 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.60 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ) ) }.
% 0.99/1.60 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 0.99/1.60 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.60 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 0.99/1.60 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.99/1.60 tc_Nat_Onat ), X ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.99/1.60 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.99/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.99/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.99/1.60 c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.60 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.99/1.60 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 0.99/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.99/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.99/1.60 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.99/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.99/1.60 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.99/1.60 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.60 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Nat_Onat ), Y ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Int_Oint, Z, X ) }.
% 0.99/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.99/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 0.99/1.60 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 0.99/1.60 ) }.
% 0.99/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.99/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.99/1.60 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 0.99/1.60 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 0.99/1.60 ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.99/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 0.99/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 0.99/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.60 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.99/1.60 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.99/1.60 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol11( Z, Y ) ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.99/1.60 , hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, U, hAPP(
% 0.99/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Int_Oint, skol11( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.60 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.99/1.60 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.99/1.60 tc_Int_Oint, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.99/1.60 , Z ), X ) ) ) ) }.
% 0.99/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.99/1.60 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 0.99/1.60 , c_Divides_Odiv__class_Odiv( X, Y, Z ), c_Divides_Odiv__class_Odiv( X, T
% 0.99/1.60 , Z ) ), c_Rings_Odvd__class_Odvd( X, Y, T ) }.
% 0.99/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.99/1.60 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 0.99/1.60 , Y, T ), c_Rings_Odvd__class_Odvd( X, c_Divides_Odiv__class_Odiv( X, Y,
% 0.99/1.60 Z ), c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.99/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.99/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 0.99/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.99/1.60 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.99/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.60 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 }.
% 0.99/1.60 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.60 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y,
% 0.99/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.99/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.99/1.60 ( tc_Int_Oint, Y ), X ) }.
% 0.99/1.60 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.99/1.60 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.99/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) }.
% 0.99/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.99/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 0.99/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.99/1.60 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Int_Oint ), Y ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.60 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.60 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.99/1.60 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.99/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.60 tc_Int_Oint, X, Y ) ) }.
% 0.99/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.99/1.60 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.99/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.99/1.60 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.99/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 0.99/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 0.99/1.60 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.99/1.60 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.99/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.60 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.99/1.60 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 0.99/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.60 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.99/1.60 }.
% 0.99/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.99/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.99/1.60 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = Y }.
% 0.99/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.99/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 0.99/1.60 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = c_Divides_Odiv__class_Odiv( X,
% 0.99/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.99/1.60 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.99/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.60 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), Z ) = Y }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.99/1.61 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.99/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.99/1.61 ), ! c_Rings_Odvd__class_Odvd( X, U, T ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.99/1.61 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 0.99/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.99/1.61 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Divides_Odiv__class_Odiv( X
% 0.99/1.61 , c_Groups_Oplus__class_Oplus( X, Y, T ), Z ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Y, Z ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.99/1.61 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( X, Y, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.99/1.61 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 0.99/1.61 , Z ) ) }.
% 0.99/1.61 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z
% 0.99/1.61 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 0.99/1.61 , Z ) ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.99/1.61 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.99/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.99/1.61 ( c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 0.99/1.61 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha13( X, Y ) }.
% 0.99/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.61 { ! alpha13( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.61 { ! alpha13( X, Y ), alpha28( X, Y ), alpha35( X, Y ) }.
% 0.99/1.61 { ! alpha28( X, Y ), alpha13( X, Y ) }.
% 0.99/1.61 { ! alpha35( X, Y ), alpha13( X, Y ) }.
% 0.99/1.61 { ! alpha35( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.61 { ! alpha35( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha35( X, Y ) }.
% 0.99/1.61 { ! alpha28( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.99/1.61 { ! alpha28( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha28( X, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Int_Oint, Y, X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.99/1.61 , Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.99/1.61 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Int_Oint, Y, X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Int_Oint ), Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Int_Oint, X, Y ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.61 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 0.99/1.61 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Int_Oint, Y, X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.61 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Int_Oint, X, Y ), X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 0.99/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Int_Oint, Z, Y ), X ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.99/1.61 ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.99/1.61 ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 0.99/1.61 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.99/1.61 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 0.99/1.61 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.99/1.61 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! c_Divides_Odiv__class_Odiv( X
% 0.99/1.61 , Z, Y ) = T, Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y
% 0.99/1.61 ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! Z = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), c_Divides_Odiv__class_Odiv
% 0.99/1.61 ( X, Z, Y ) = T }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 0.99/1.61 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), !
% 0.99/1.61 c_Divides_Odiv__class_Odiv( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U
% 0.99/1.61 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP(
% 0.99/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 0.99/1.61 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), ! hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 0.99/1.61 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 0.99/1.61 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.99/1.61 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.99/1.61 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.99/1.61 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.99/1.61 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.99/1.61 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.99/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.99/1.61 alpha14( X, Z ) }.
% 0.99/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.99/1.61 alpha29( X, Y, Z ) }.
% 0.99/1.61 { ! alpha14( X, Z ), ! alpha29( X, Y, Z ), hBOOL( hAPP( Z,
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 0.99/1.61 { ! alpha29( X, Y, Z ), alpha36( X, Y, Z ) }.
% 0.99/1.61 { ! alpha29( X, Y, Z ), alpha40( X, Y, Z ) }.
% 0.99/1.61 { ! alpha36( X, Y, Z ), ! alpha40( X, Y, Z ), alpha29( X, Y, Z ) }.
% 0.99/1.61 { ! alpha40( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha45( X, Y, Z ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha40( X, Y, Z ) }.
% 0.99/1.61 { ! alpha45( X, Y, Z ), alpha40( X, Y, Z ) }.
% 0.99/1.61 { ! alpha45( X, Y, Z ), ! alpha49( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.99/1.61 { ! hBOOL( hAPP( Z, skol12( T, U, Z ) ) ), alpha45( X, Y, Z ) }.
% 0.99/1.61 { alpha49( X, Y, skol12( X, Y, Z ) ), alpha45( X, Y, Z ) }.
% 0.99/1.61 { ! alpha49( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.61 skol13( X, T, U ) ) }.
% 0.99/1.61 { ! alpha49( X, Y, Z ), alpha53( X, Y, Z, skol13( X, Y, Z ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha53( X, Y, Z
% 0.99/1.61 , T ), alpha49( X, Y, Z ) }.
% 0.99/1.61 { ! alpha53( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.61 { ! alpha53( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.99/1.61 .
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha53( X,
% 0.99/1.61 Y, Z, T ) }.
% 0.99/1.61 { ! alpha36( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha41( X, Y, Z ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Int_Oint ), X ), alpha36( X, Y, Z ) }.
% 0.99/1.61 { ! alpha41( X, Y, Z ), alpha36( X, Y, Z ) }.
% 0.99/1.61 { ! alpha41( X, Y, Z ), ! alpha46( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.99/1.61 { ! hBOOL( hAPP( Z, skol14( T, U, Z ) ) ), alpha41( X, Y, Z ) }.
% 0.99/1.61 { alpha46( X, Y, skol14( X, Y, Z ) ), alpha41( X, Y, Z ) }.
% 0.99/1.61 { ! alpha46( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol15( T, U, W ) ) }.
% 0.99/1.61 { ! alpha46( X, Y, Z ), alpha50( X, Y, Z, skol15( X, Y, Z ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha50( X, Y, Z, T )
% 0.99/1.61 , alpha46( X, Y, Z ) }.
% 0.99/1.61 { ! alpha50( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.99/1.61 ) }.
% 0.99/1.61 { ! alpha50( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.99/1.61 .
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha50( X,
% 0.99/1.61 Y, Z, T ) }.
% 0.99/1.61 { ! alpha14( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.99/1.61 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.99/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha14( X, Y ) }.
% 0.99/1.61 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha14
% 0.99/1.61 ( X, Y ) }.
% 0.99/1.61 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha56( X,
% 0.99/1.61 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Int_Oint, T, Z ) = Y }.
% 0.99/1.61 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha56( X,
% 0.99/1.61 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Int_Oint, T, Z ) = Y }.
% 0.99/1.61 { ! alpha56( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.99/1.61 { ! alpha56( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha56( X, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.99/1.61 , alpha56( X, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3div( X, Y ) =
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3div( X, Y ) =
% 0.99/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.99/1.61 ( tc_Int_Oint, X, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) }
% 0.99/1.61 .
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol16( Z, Y ) ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.99/1.61 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 0.99/1.61 tc_Int_Oint, skol16( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.99/1.61 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.99/1.61 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 0.99/1.61 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 0.99/1.61 ) ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) }.
% 0.99/1.61 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.99/1.61 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.99/1.61 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.99/1.61 ( X ), Z, Y ) ) }.
% 0.99/1.61 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.99/1.61 tc_Polynomial_Opoly( X ), Y ) ) = c_Groups_Ouminus__class_Ouminus(
% 0.99/1.61 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.99/1.61 ( X ), Z, Y ) ) }.
% 0.99/1.61 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.99/1.61 ( X ), T, Z ), Y ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Nat_Onat, Z, Y ), X ) }.
% 0.99/1.61 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.61 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.99/1.61 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.99/1.61 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Nat_Onat, Y, X ), Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.99/1.61 ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.99/1.61 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.99/1.61 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.99/1.61 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.99/1.61 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.99/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.99/1.61 alpha15( X, Z ) }.
% 0.99/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.99/1.61 alpha30( X, Y, Z ) }.
% 0.99/1.61 { ! alpha15( X, Z ), ! alpha30( X, Y, Z ), hBOOL( hAPP( Z,
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 0.99/1.61 { ! alpha30( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.61 alpha37( X, Y, Z ) }.
% 0.99/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha30( X, Y, Z ) }.
% 0.99/1.61 { ! alpha37( X, Y, Z ), alpha30( X, Y, Z ) }.
% 0.99/1.61 { ! alpha37( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.99/1.61 ), alpha42( X, Y, Z, T ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol17( X, T, U ), X ),
% 0.99/1.61 alpha37( X, Y, Z ) }.
% 0.99/1.61 { ! alpha42( X, Y, Z, skol17( X, Y, Z ) ), alpha37( X, Y, Z ) }.
% 0.99/1.61 { ! alpha42( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.99/1.61 hBOOL( hAPP( Z, U ) ) }.
% 0.99/1.61 { ! hBOOL( hAPP( Z, skol18( U, W, Z, V0 ) ) ), alpha42( X, Y, Z, T ) }.
% 0.99/1.61 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol18( X, Y, Z, T ) )
% 0.99/1.61 , T ), alpha42( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha15( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.61 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.99/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha15( X, Y ) }.
% 0.99/1.61 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha15
% 0.99/1.61 ( X, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ),
% 0.99/1.61 ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ), Z
% 0.99/1.61 = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 0.99/1.61 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 0.99/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ) }
% 0.99/1.61 .
% 0.99/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.99/1.61 alpha16( X, Z ), alpha31( X, Y, Z ) }.
% 0.99/1.61 { ! alpha16( X, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Nat_Onat, Y, X ) ) ) }.
% 0.99/1.61 { ! alpha31( X, Y, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Nat_Onat, Y, X ) ) ) }.
% 0.99/1.61 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol19( X
% 0.99/1.61 , Y, T ) ), Y ) }.
% 0.99/1.61 { ! alpha31( X, Y, Z ), alpha38( X, Y, Z, skol19( X, Y, Z ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), T ), Y ), ! alpha38( X
% 0.99/1.61 , Y, Z, T ), alpha31( X, Y, Z ) }.
% 0.99/1.61 { ! alpha38( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc
% 0.99/1.61 ( T ) ) ) }.
% 0.99/1.61 { ! alpha38( X, Y, Z, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( T ) ) ), !
% 0.99/1.61 hBOOL( hAPP( Z, T ) ), alpha38( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha16( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.61 { ! alpha16( X, Y ), hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Nat_Onat ) ) ) }.
% 0.99/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha16( X, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.99/1.61 , Y ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.99/1.61 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.99/1.61 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.99/1.61 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol20( Z, Y
% 0.99/1.61 ), Y ) }.
% 0.99/1.61 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.99/1.61 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.99/1.61 skol20( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.99/1.61 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.99/1.61 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.99/1.61 , skol20( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha17( X, Y, T,
% 0.99/1.61 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha17( X, Y, skol21( X, Y
% 0.99/1.61 , Z ), skol29( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.99/1.61 skol21( X, Y, Z ) ), skol29( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.99/1.61 { ! alpha17( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T
% 0.99/1.61 ) }.
% 0.99/1.61 { ! alpha17( X, Y, Z, T ), alpha32( X, Y, Z, T ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha32( X, Y, Z
% 0.99/1.61 , T ), alpha17( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha32( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.61 { ! alpha32( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.99/1.61 .
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha32( X,
% 0.99/1.61 Y, Z, T ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Int_Oint ) ) = X }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.99/1.61 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( X ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.99/1.61 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.61 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Int_Oint, Z, X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.61 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, X ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 c_Divides_Odiv__class_Omod( X, Z, Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 0.99/1.61 ), Y ) ) = Z }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), c_Divides_Odiv__class_Omod( X, Y
% 0.99/1.61 , Z ) ) = Y }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X
% 0.99/1.61 , Z, Y ) ), Y ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.61 ( X ), T ), c_Divides_Odiv__class_Odiv( X, Z, T ) ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( X, Z, T ) ), Y ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.61 ( X ), c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.99/1.61 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.61 X ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.99/1.61 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.61 X ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 0.99/1.61 Z ) = c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.99/1.61 ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.99/1.61 ), ! c_Rings_Odvd__class_Odvd( X, Z, c_Divides_Odiv__class_Omod( X, T, Y
% 0.99/1.61 ) ), c_Rings_Odvd__class_Odvd( X, Z, T ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.99/1.61 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 0.99/1.61 , c_Divides_Odiv__class_Omod( X, T, Y ) ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.99/1.61 ), c_Divides_Odiv__class_Omod( X, c_Divides_Odiv__class_Omod( X, T, Y )
% 0.99/1.61 , Z ) = c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.99/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.99/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.99/1.61 tc_Int_Oint, Y, c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.99/1.61 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 0.99/1.61 , c_Divides_Odiv__class_Omod( X, Y, T ) ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, T,
% 0.99/1.61 c_Divides_Odiv__class_Omod( X, Z, Y ) ), ! c_Rings_Odvd__class_Odvd( X, T
% 0.99/1.61 , Y ), c_Rings_Odvd__class_Odvd( X, T, Z ) }.
% 0.99/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Divides_Odiv__class_Omod(
% 0.99/1.61 tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X ),
% 0.99/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.99/1.61 ( tc_Int_Oint, Y, X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.99/1.61 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol22( X, Y ) ) }.
% 0.99/1.61 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 0.99/1.61 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.99/1.61 ( tc_Int_Oint, Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.99/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 0.99/1.61 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.99/1.61 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 0.99/1.61 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.99/1.61 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 0.99/1.61 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.99/1.61 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 0.99/1.61 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 0.99/1.61 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 0.99/1.61 , U ), Z ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.99/1.61 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ), X ), Y ) =
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.99/1.61 tc_Int_Oint, Z, X ), Y ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.99/1.61 tc_Int_Oint, Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.99/1.61 tc_Int_Oint, Z, Y ), X ) }.
% 0.99/1.61 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.99/1.61 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.99/1.61 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.99/1.61 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 0.99/1.61 Y ) ), Y ) }.
% 0.99/1.61 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.99/1.61 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.99/1.61 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.99/1.61 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 0.99/1.61 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.99/1.61 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.99/1.61 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.99/1.61 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.99/1.61 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.61 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.99/1.61 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.61 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.99/1.61 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.61 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 0.99/1.61 , Y ) ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.99/1.61 ), Z ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 0.99/1.61 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.99/1.61 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.99/1.61 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.61 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.99/1.61 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 0.99/1.61 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 0.99/1.61 }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.99/1.61 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 0.99/1.61 X, Z, Y ) }.
% 0.99/1.61 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.99/1.61 = c_Divides_Odiv__class_Omod( X, Y, Z ), c_Divides_Odiv__class_Omod( X,
% 0.99/1.61 c_Groups_Ouminus__class_Ouminus( X, T ), Z ) = c_Divides_Odiv__class_Omod
% 0.99/1.61 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.99/1.61 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.99/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.99/1.61 ( X, c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Omod( X, Z
% 0.99/1.61 , Y ) ), Y ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.99/1.61 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.99/1.61 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 0.99/1.61 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 0.99/1.61 ), Z ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 0.99/1.61 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 T, Y ), Z ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.99/1.61 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.99/1.61 T, Z ), Y ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.99/1.61 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.99/1.61 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.99/1.61 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.99/1.61 ), Z ), Y ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.99/1.61 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 0.99/1.61 , Y ) ), Y ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.99/1.61 ( X, Y, Z ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 0.99/1.61 ( X, Z, Y ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.99/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.99/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.61 }.
% 0.99/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.99/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.99/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.99/1.61 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) ) }
% 0.99/1.61 .
% 0.99/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.99/1.61 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.99/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.99/1.61 ( tc_Int_Oint, Y, X ) ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.99/1.61 ( tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.99/1.61 ( tc_Int_Oint, Y ), X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.99/1.61 tc_Int_Oint, X, Y ) ) }.
% 0.99/1.61 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) =
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), c_Rings_Odvd__class_Odvd
% 0.99/1.61 ( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, X ) ) }
% 0.99/1.61 .
% 0.99/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus
% 0.99/1.61 ( tc_Int_Oint, Z, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y )
% 0.99/1.61 = c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.99/1.61 tc_Int_Oint, Y, X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.99/1.61 tc_Int_Oint, Y, X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.99/1.61 ( tc_Int_Oint, Y, X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.99/1.61 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.99/1.61 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.99/1.61 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.99/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.99/1.61 ( tc_Int_Oint, Y, X ) ) }.
% 0.99/1.61 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.99/1.61 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.99/1.61 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.99/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.99/1.61 tc_Int_Oint, Y, X ), X ) }.
% 0.99/1.61 { Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.99/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.99/1.61 ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ), X ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) }.
% 0.99/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, Y ) ), Y ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) ), X ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.99/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 0.99/1.61 ( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.99/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) =
% 0.99/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.99/1.61 ( tc_Int_Oint, X, Y ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Omod
% 0.99/1.61 ( tc_Int_Oint, X, Y ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y )
% 0.99/1.61 }.
% 0.99/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 0.99/1.61 alpha18( X, Y, Z ) }.
% 0.99/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 0.99/1.61 alpha33( X, Y, Z ) }.
% 0.99/1.61 { ! alpha18( X, Y, Z ), ! alpha33( X, Y, Z ), hBOOL( hAPP( Z,
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.99/1.61 { ! alpha33( X, Y, Z ), alpha39( X, Y, Z ) }.
% 0.99/1.61 { ! alpha33( X, Y, Z ), alpha43( X, Y, Z ) }.
% 0.99/1.61 { ! alpha39( X, Y, Z ), ! alpha43( X, Y, Z ), alpha33( X, Y, Z ) }.
% 0.99/1.61 { ! alpha43( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha47( X, Y, Z ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha43( X, Y, Z ) }.
% 0.99/1.61 { ! alpha47( X, Y, Z ), alpha43( X, Y, Z ) }.
% 0.99/1.61 { ! alpha47( X, Y, Z ), ! alpha51( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.99/1.61 { ! hBOOL( hAPP( Z, skol23( T, U, Z ) ) ), alpha47( X, Y, Z ) }.
% 0.99/1.61 { alpha51( X, Y, skol23( X, Y, Z ) ), alpha47( X, Y, Z ) }.
% 0.99/1.61 { ! alpha51( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z )
% 0.99/1.61 }.
% 0.99/1.61 { ! alpha51( X, Y, Z ), alpha54( X, Y, Z ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), ! alpha54( X, Y, Z
% 0.99/1.61 ), alpha51( X, Y, Z ) }.
% 0.99/1.61 { ! alpha54( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.61 { ! alpha54( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol24( X, Y,
% 0.99/1.61 Z ) ), Z ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha54( X,
% 0.99/1.61 Y, Z ) }.
% 0.99/1.61 { ! alpha39( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha44( X, Y, Z ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.61 tc_Int_Oint ), X ), alpha39( X, Y, Z ) }.
% 0.99/1.61 { ! alpha44( X, Y, Z ), alpha39( X, Y, Z ) }.
% 0.99/1.61 { ! alpha44( X, Y, Z ), ! alpha48( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.99/1.61 { ! hBOOL( hAPP( Z, skol25( T, U, Z ) ) ), alpha44( X, Y, Z ) }.
% 0.99/1.61 { alpha48( X, Y, skol25( X, Y, Z ) ), alpha44( X, Y, Z ) }.
% 0.99/1.61 { ! alpha48( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ) }.
% 0.99/1.61 { ! alpha48( X, Y, Z ), alpha52( X, Y, Z ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! alpha52( X, Y, Z ),
% 0.99/1.61 alpha48( X, Y, Z ) }.
% 0.99/1.61 { ! alpha52( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X )
% 0.99/1.61 }.
% 0.99/1.61 { ! alpha52( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 0.99/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol26( X, Y,
% 0.99/1.61 Z ) ), Z ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), ! Y =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha52( X,
% 0.99/1.61 Y, Z ) }.
% 0.99/1.61 { ! alpha18( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.99/1.61 hBOOL( hAPP( Z, Y ) ) }.
% 0.99/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha18( X, Y, Z ) }.
% 0.99/1.61 { ! hBOOL( hAPP( Z, Y ) ), alpha18( X, Y, Z ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.99/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.99/1.61 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.99/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.99/1.61 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ), hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ),
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 0.99/1.61 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ),
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.61 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha57( X,
% 0.99/1.61 Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.99/1.61 tc_Int_Oint, Z, Y ) = X }.
% 0.99/1.61 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha57( X,
% 0.99/1.61 Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.99/1.61 tc_Int_Oint, Z, Y ) = X }.
% 0.99/1.61 { ! alpha57( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.99/1.61 { ! alpha57( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.99/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha57( X, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.99/1.61 , alpha57( X, Y ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, hAPP(
% 0.99/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Int_Oint, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y
% 0.99/1.61 ) ) }.
% 0.99/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.99/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.99/1.61 ( tc_Int_Oint, Y, X ) ) }.
% 0.99/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.99/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.99/1.61 ( tc_Int_Oint, Y, X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.99/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.99/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.99/1.61 ( tc_Int_Oint, Y, X ) ) }.
% 0.99/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.99/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.99/1.61 ( tc_Int_Oint, Y, X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv
% 0.99/1.61 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X )
% 0.99/1.61 ) ), ! alpha19( X, Y, T, U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), X ), alpha19( X, Y, skol27( X, Y, Z ), skol30( X, Y, Z )
% 0.99/1.61 ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X )
% 0.99/1.61 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, skol27( X, Y, Z ) ), skol30
% 0.99/1.61 ( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 0.99/1.61 ) }.
% 0.99/1.61 { ! alpha19( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ) }.
% 0.99/1.61 { ! alpha19( X, Y, Z, T ), alpha34( X, Y, Z, T ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha34( X, Y, Z, T )
% 0.99/1.61 , alpha19( X, Y, Z, T ) }.
% 0.99/1.61 { ! alpha34( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.99/1.61 ) }.
% 0.99/1.61 { ! alpha34( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.99/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.99/1.61 .
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha34( X,
% 0.99/1.61 Y, Z, T ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3mod( X, Y ) =
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) }.
% 0.99/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3mod( X, Y ) =
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, X,
% 0.99/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.99/1.61 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.99/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 0.99/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 0.99/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ),
% 0.99/1.61 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Int_Oint, X, Y ) ) = c_Divides_Odiv__class_Odiv( tc_Int_Oint,
% 0.99/1.61 c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ), c_Groups_Oabs__class_Oabs(
% 0.99/1.61 tc_Int_Oint, Y ) ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.99/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Divides_Odiv__class_Odiv
% 0.99/1.61 ( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.99/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Y ) ) =
% 0.99/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Divides_Odiv__class_Omod
% 0.99/1.61 ( tc_Nat_Onat, X, Y ) ) }.
% 0.99/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ), X ) =
% 0.99/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Divides_Odiv__class_Omod
% 0.99/1.61 ( tc_Nat_Onat, Y, X ) ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.61 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Nat_Onat, Z, X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.61 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, X ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.99/1.61 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.99/1.61 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.99/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.99/1.61 tc_Nat_Onat, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y
% 0.99/1.61 ) ) }.
% 0.99/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ),
% 0.99/1.61 class_Groups_Ocancel__ab__semigroup__add( X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Groups_Ocancel__semigroup__add(
% 0.99/1.61 X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Groups_Oab__semigroup__mult( X )
% 0.99/1.61 }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Groups_Ocomm__monoid__mult( X )
% 0.99/1.61 }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Groups_Oab__semigroup__add( X )
% 0.99/1.61 }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Groups_Ocomm__monoid__add( X ) }
% 0.99/1.61 .
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__semiring__1( X ) }
% 0.99/1.61 .
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__semiring__0( X ) }
% 0.99/1.61 .
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__semiring( X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Groups_Oab__group__add( X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ozero__neq__one( X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Groups_Omonoid__mult( X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Groups_Omonoid__add( X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Osemiring__0( X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Groups_Ogroup__add( X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Omult__zero( X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring( X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Osemiring( X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Groups_Ouminus( X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1( X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Groups_Ominus( X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Power_Opower( X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Groups_Ozero( X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring( X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Groups_Oone( X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Odvd( X ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ),
% 0.99/1.61 class_Groups_Ocancel__comm__monoid__add( X ) }.
% 0.99/1.61 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.99/1.61 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.99/1.61 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.99/1.61 ( tc_fun( Y, X ) ) }.
% 0.99/1.61 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.99/1.61 ) ) }.
% 0.99/1.61 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.99/1.61 .
% 0.99/1.61 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.99/1.61 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.99/1.61 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.99/1.61 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.61 tc_Int_Oint ) }.
% 0.99/1.61 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.61 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.99/1.61 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.61 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.99/1.61 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.99/1.61 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.99/1.61 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.99/1.61 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.99/1.61 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.99/1.61 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.99/1.61 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.99/1.61 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.99/1.61 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.99/1.61 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.99/1.61 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.99/1.61 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.99/1.61 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.99/1.61 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.99/1.61 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.99/1.61 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.99/1.61 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.99/1.61 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.99/1.61 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.99/1.61 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.99/1.61 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.99/1.61 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.99/1.61 { class_Power_Opower( tc_Int_Oint ) }.
% 0.99/1.61 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.99/1.61 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.99/1.61 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.99/1.61 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.61 tc_Nat_Onat ) }.
% 0.99/1.61 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.99/1.61 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.99/1.61 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.99/1.61 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.99/1.61 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.99/1.61 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.99/1.61 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.99/1.61 { ! class_Rings_Oidom( X ),
% 0.99/1.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.61 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.99/1.61 ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.61 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.99/1.61 X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.61 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.99/1.61 ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.61 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.99/1.61 }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.61 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.61 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.61 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.61 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.99/1.61 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.61 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.61 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.61 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.61 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.61 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.99/1.61 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.99/1.61 ( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.99/1.61 ( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 0.99/1.61 ( X ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.99/1.61 }.
% 0.99/1.61 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.99/1.61 ) ) }.
% 0.99/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.99/1.61 .
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.99/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.61 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 0.99/1.61 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 0.99/1.61 { ! hAPP( c_Polynomial_Opoly( t_a, hAPP( hAPP(
% 0.99/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( t_a ) ),
% 0.99/1.61 c_Polynomial_Omonom( t_a, c_Groups_Oone__class_Oone( t_a ), v_n ) ), v_p
% 0.99/1.61 ) ), v_x ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( t_a ), hAPP(
% 0.99/1.61 hAPP( c_Power_Opower__class_Opower( t_a ), v_x ), v_n ) ), hAPP(
% 0.99/1.61 c_Polynomial_Opoly( t_a, v_p ), v_x ) ) }.
% 0.99/1.61 { class_Rings_Ocomm__ring__1( t_a ) }.
% 0.99/1.61
% 0.99/1.61 *** allocated 15000 integers for clauses
% 0.99/1.61 *** allocated 22500 integers for clauses
% 0.99/1.61 *** allocated 33750 integers for clauses
% 0.99/1.61 *** allocated 50625 integers for clauses
% 0.99/1.61 *** allocated 75937 integers for clauses
% 0.99/1.61 percentage equality = 0.258657, percentage horn = 0.904731
% 0.99/1.61 This is a problem with some equality
% 0.99/1.61
% 0.99/1.61
% 0.99/1.61
% 0.99/1.61 Options Used:
% 0.99/1.61
% 0.99/1.61 useres = 1
% 0.99/1.61 useparamod = 1
% 0.99/1.61 useeqrefl = 1
% 0.99/1.61 useeqfact = 1
% 0.99/1.61 usefactor = 1
% 0.99/1.61 usesimpsplitting = 0
% 0.99/1.61 usesimpdemod = 5
% 0.99/1.61 usesimpres = 3
% 0.99/1.61
% 0.99/1.61 resimpinuse = 1000
% 0.99/1.61 resimpclauses = 20000
% 0.99/1.61 substype = eqrewr
% 0.99/1.61 backwardsubs = 1
% 0.99/1.61 selectoldest = 5
% 0.99/1.61
% 0.99/1.61 litorderings [0] = split
% 0.99/1.61 litorderings [1] = extend the termordering, first sorting on arguments
% 0.99/1.61
% 0.99/1.61 termordering = kbo
% 0.99/1.61
% 0.99/1.61 litapriori = 0
% 0.99/1.61 termapriori = 1
% 0.99/1.61 litaposteriori = 0
% 0.99/1.61 termaposteriori = 0
% 0.99/1.61 demodaposteriori = 0
% 0.99/1.61 ordereqreflfact = 0
% 0.99/1.61
% 0.99/1.61 litselect = negord
% 0.99/1.61
% 0.99/1.61 maxweight = 15
% 0.99/1.61 maxdepth = 30000
% 0.99/1.61 maxlength = 115
% 0.99/1.61 maxnrvars = 195
% 0.99/1.61 excuselevel = 1
% 0.99/1.61 increasemaxweight = 1
% 0.99/1.61
% 0.99/1.61 maxselected = 10000000
% 0.99/1.61 maxnrclauses = 10000000
% 0.99/1.61
% 0.99/1.61 showgenerated = 0
% 0.99/1.61 showkept = 0
% 0.99/1.61 showselected = 0
% 0.99/1.61 showdeleted = 0
% 0.99/1.61 showresimp = 1
% 0.99/1.61 showstatus = 2000
% 0.99/1.61
% 0.99/1.61 prologoutput = 0
% 0.99/1.61 nrgoals = 5000000
% 0.99/1.61 totalproof = 1
% 0.99/1.61
% 0.99/1.61 Symbols occurring in the translation:
% 0.99/1.61
% 0.99/1.61 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.99/1.61 . [1, 2] (w:1, o:182, a:1, s:1, b:0),
% 0.99/1.61 ! [4, 1] (w:0, o:102, a:1, s:1, b:0),
% 0.99/1.61 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.99/1.61 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.99/1.61 hAPP [38, 2] (w:1, o:206, a:1, s:1, b:0),
% 0.99/1.61 class_Rings_Ocomm__semiring__1 [43, 1] (w:1, o:110, a:1, s:1, b:0),
% 0.99/1.61 c_Polynomial_Omonom [44, 3] (w:1, o:244, a:1, s:1, b:0),
% 0.99/1.61 c_Polynomial_Opoly [45, 2] (w:1, o:207, a:1, s:1, b:0),
% 0.99/1.61 c_Groups_Otimes__class_Otimes [46, 1] (w:1, o:111, a:1, s:1, b:0),
% 0.99/1.61 c_Power_Opower__class_Opower [47, 1] (w:1, o:112, a:1, s:1, b:0),
% 0.99/1.61 class_Rings_Ocomm__semiring__0 [50, 1] (w:1, o:109, a:1, s:1, b:0),
% 0.99/1.61 tc_Polynomial_Opoly [51, 1] (w:1, o:114, a:1, s:1, b:0),
% 0.99/1.61 c_Groups_Oone__class_Oone [52, 1] (w:1, o:115, a:1, s:1, b:0),
% 0.99/1.61 class_Groups_Omonoid__mult [53, 1] (w:1, o:118, a:1, s:1, b:0),
% 0.99/1.61 class_Groups_Ocomm__monoid__mult [55, 1] (w:1, o:119, a:1, s:1, b:0)
% 0.99/1.61 ,
% 0.99/1.61 tc_Nat_Onat [57, 0] (w:1, o:47, a:1, s:1, b:0),
% 0.99/1.61 class_Groups_Oab__semigroup__mult [64, 1] (w:1, o:120, a:1, s:1, b:0)
% 0.99/1.61 ,
% 0.99/1.61 class_Groups_Oone [67, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.99/1.61 class_Int_Oring__char__0 [70, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.99/1.61 class_Rings_Oidom [71, 1] (w:1, o:123, a:1, s:1, b:0),
% 0.99/1.61 class_Groups_Ozero [75, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.99/1.61 class_Power_Opower [76, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.99/1.61 c_Power_Opower_Opower [77, 3] (w:1, o:245, a:1, s:1, b:0),
% 0.99/1.61 c_Groups_Oplus__class_Oplus [78, 3] (w:1, o:246, a:1, s:1, b:0),
% 0.99/1.61 class_Lattices_Oab__semigroup__idem__mult [79, 1] (w:1, o:130, a:1
% 0.99/1.61 , s:1, b:0),
% 0.99/1.61 class_Rings_Olinordered__semidom [80, 1] (w:1, o:133, a:1, s:1, b:0)
% 0.99/1.61 ,
% 0.99/1.61 c_Orderings_Oord__class_Oless [81, 3] (w:1, o:242, a:1, s:1, b:0),
% 0.99/1.61 c_Polynomial_Opcompose [82, 3] (w:1, o:248, a:1, s:1, b:0),
% 0.99/1.61 class_Rings_Oring__1 [83, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.99/1.61 c_Groups_Ouminus__class_Ouminus [84, 2] (w:1, o:209, a:1, s:1, b:0),
% 0.99/1.61
% 0.99/1.61 class_Rings_Olinordered__idom [85, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.99/1.61 c_Polynomial_Opos__poly [86, 2] (w:1, o:210, a:1, s:1, b:0),
% 0.99/1.61 c_Groups_Ozero__class_Ozero [87, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.99/1.61 class_Groups_Ogroup__add [88, 1] (w:1, o:137, a:1, s:1, b:0),
% 0.99/1.61 class_Groups_Oab__group__add [89, 1] (w:1, o:138, a:1, s:1, b:0),
% 0.99/1.61 class_Groups_Omonoid__add [90, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.99/1.61 class_Groups_Ocomm__monoid__add [91, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.99/1.61
% 0.99/1.61 class_Groups_Oordered__ab__group__add [92, 1] (w:1, o:141, a:1, s:1
% 0.99/1.61 , b:0),
% 0.99/1.61 class_Groups_Olinordered__ab__group__add [93, 1] (w:1, o:117, a:1, s:
% 0.99/1.61 1, b:0),
% 0.99/1.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [94
% 0.99/1.61 , 1] (w:1, o:165, a:1, s:1, b:0),
% 0.99/1.61 class_Groups_Oab__semigroup__add [96, 1] (w:1, o:166, a:1, s:1, b:0)
% 0.99/1.61 ,
% 0.99/1.61 class_Groups_Ocancel__semigroup__add [98, 1] (w:1, o:167, a:1, s:1
% 0.99/1.61 , b:0),
% 0.99/1.61 class_Groups_Oordered__ab__semigroup__add__imp__le [99, 1] (w:1, o:
% 0.99/1.61 168, a:1, s:1, b:0),
% 0.99/1.61 class_Groups_Oordered__comm__monoid__add [102, 1] (w:1, o:169, a:1
% 0.99/1.61 , s:1, b:0),
% 0.99/1.61 class_Groups_Oordered__cancel__ab__semigroup__add [104, 1] (w:1, o:
% 0.99/1.61 170, a:1, s:1, b:0),
% 0.99/1.61 class_Groups_Ocancel__ab__semigroup__add [105, 1] (w:1, o:171, a:1
% 0.99/1.61 , s:1, b:0),
% 0.99/1.61 class_Lattices_Oboolean__algebra [107, 1] (w:1, o:172, a:1, s:1, b:0)
% 0.99/1.61 ,
% 0.99/1.61 class_Groups_Ouminus [110, 1] (w:1, o:173, a:1, s:1, b:0),
% 0.99/1.61 tc_fun [111, 2] (w:1, o:220, a:1, s:1, b:0),
% 0.99/1.61 class_Rings_Omult__zero [113, 1] (w:1, o:147, a:1, s:1, b:0),
% 0.99/1.61 class_Rings_Ono__zero__divisors [114, 1] (w:1, o:148, a:1, s:1, b:0)
% 0.99/1.61 ,
% 0.99/1.61 class_Rings_Ozero__neq__one [115, 1] (w:1, o:149, a:1, s:1, b:0),
% 0.99/1.61 class_Rings_Ocomm__ring [116, 1] (w:1, o:107, a:1, s:1, b:0),
% 0.99/1.61 class_Rings_Osemiring__0 [118, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.99/1.61 class_Rings_Oring__1__no__zero__divisors [123, 1] (w:1, o:150, a:1
% 0.99/1.61 , s:1, b:0),
% 0.99/1.61 class_Rings_Ocomm__ring__1 [124, 1] (w:1, o:108, a:1, s:1, b:0),
% 0.99/1.61 class_Rings_Olinordered__ring [126, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.99/1.61 class_Rings_Olinordered__ring__strict [127, 1] (w:1, o:132, a:1, s:1
% 0.99/1.61 , b:0),
% 0.99/1.61 hBOOL [129, 1] (w:1, o:174, a:1, s:1, b:0),
% 0.99/1.61 class_Rings_Oring__no__zero__divisors [136, 1] (w:1, o:151, a:1, s:1
% 0.99/1.61 , b:0),
% 0.99/1.61 class_Rings_Osemiring [138, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.99/1.61 class_Rings_Ocomm__semiring [139, 1] (w:1, o:155, a:1, s:1, b:0),
% 0.99/1.61 class_Rings_Oring [140, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.99/1.61 class_Rings_Olinordered__comm__semiring__strict [141, 1] (w:1, o:142
% 0.99/1.61 , a:1, s:1, b:0),
% 0.99/1.61 class_Rings_Olinordered__semiring__strict [142, 1] (w:1, o:143, a:1
% 0.99/1.61 , s:1, b:0),
% 0.99/1.61 c_Polynomial_Oorder [143, 3] (w:1, o:247, a:1, s:1, b:0),
% 0.99/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [145, 2] (w:1, o:
% 0.99/1.61 208, a:1, s:1, b:0),
% 0.99/1.61 tc_Int_Oint [146, 0] (w:1, o:81, a:1, s:1, b:0),
% 0.99/1.61 class_RealVector_Oreal__normed__algebra [147, 1] (w:1, o:156, a:1, s:
% 0.99/1.61 1, b:0),
% 0.99/1.61 c_Orderings_Oord__class_Oless__eq [156, 3] (w:1, o:243, a:1, s:1, b:0
% 0.99/1.61 ),
% 0.99/1.61 c_Groups_Ominus__class_Ominus [157, 3] (w:1, o:249, a:1, s:1, b:0),
% 0.99/1.61 class_Rings_Olinordered__semiring__1__strict [159, 1] (w:1, o:144, a:
% 0.99/1.61 1, s:1, b:0),
% 0.99/1.61 c_Groups_Osgn__class_Osgn [160, 2] (w:1, o:221, a:1, s:1, b:0),
% 0.99/1.61 class_Groups_Osgn__if [161, 1] (w:1, o:175, a:1, s:1, b:0),
% 0.99/1.61 c_Polynomial_OpCons [162, 3] (w:1, o:250, a:1, s:1, b:0),
% 0.99/1.61 class_Groups_Ominus [166, 1] (w:1, o:176, a:1, s:1, b:0),
% 0.99/1.61 class_Rings_Oordered__ring [170, 1] (w:1, o:157, a:1, s:1, b:0),
% 0.99/1.61 class_Groups_Oordered__ab__semigroup__add [172, 1] (w:1, o:177, a:1
% 0.99/1.61 , s:1, b:0),
% 0.99/1.61 class_RealVector_Oreal__normed__vector [174, 1] (w:1, o:158, a:1, s:1
% 0.99/1.61 , b:0),
% 0.99/1.61 class_RealVector_Oreal__normed__div__algebra [175, 1] (w:1, o:159, a:
% 0.99/1.61 1, s:1, b:0),
% 0.99/1.61 class_RealVector_Oreal__normed__algebra__1 [176, 1] (w:1, o:160, a:1
% 0.99/1.61 , s:1, b:0),
% 0.99/1.61 class_Rings_Oordered__cancel__semiring [177, 1] (w:1, o:161, a:1, s:1
% 0.99/1.61 , b:0),
% 0.99/1.61 class_Rings_Oordered__semiring [178, 1] (w:1, o:162, a:1, s:1, b:0),
% 0.99/1.61
% 0.99/1.61 class_Rings_Oordered__comm__semiring [179, 1] (w:1, o:163, a:1, s:1
% 0.99/1.61 , b:0),
% 0.99/1.61 class_Rings_Olinordered__semiring [180, 1] (w:1, o:145, a:1, s:1, b:0
% 0.99/1.61 ),
% 0.99/1.61 class_Rings_Olinordered__semiring__1 [182, 1] (w:1, o:146, a:1, s:1
% 0.99/1.61 , b:0),
% 0.99/1.61 c_Polynomial_Osynthetic__div [186, 3] (w:1, o:251, a:1, s:1, b:0),
% 0.99/1.61 class_Orderings_Opreorder [187, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.99/1.61 c_Nat__Transfer_Otsub [188, 2] (w:1, o:222, a:1, s:1, b:0),
% 0.99/1.61 class_Orderings_Oord [190, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.99/1.61 class_Orderings_Olinorder [191, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.99/1.61 class_Orderings_Oorder [192, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.99/1.61 c_Rings_Odvd__class_Odvd [193, 3] (w:1, o:252, a:1, s:1, b:0),
% 0.99/1.61 class_Rings_Odvd [194, 1] (w:1, o:164, a:1, s:1, b:0),
% 3.07/3.51 c_Nat_OSuc [197, 1] (w:1, o:178, a:1, s:1, b:0),
% 3.07/3.51 c_Divides_Odiv__class_Odiv [204, 3] (w:1, o:253, a:1, s:1, b:0),
% 3.07/3.51 c_Polynomial_Opoly__rec [205, 5] (w:1, o:319, a:1, s:1, b:0),
% 3.07/3.51 class_Divides_Osemiring__div [206, 1] (w:1, o:180, a:1, s:1, b:0),
% 3.07/3.51 class_Divides_Oring__div [207, 1] (w:1, o:179, a:1, s:1, b:0),
% 3.07/3.51 c_fequal [208, 2] (w:1, o:223, a:1, s:1, b:0),
% 3.07/3.51 c_If [209, 4] (w:1, o:305, a:1, s:1, b:0),
% 3.07/3.51 c_SMT_Oz3div [214, 2] (w:1, o:224, a:1, s:1, b:0),
% 3.07/3.51 class_Fields_Ofield [215, 1] (w:1, o:116, a:1, s:1, b:0),
% 3.07/3.51 c_Divides_Odiv__class_Omod [217, 3] (w:1, o:254, a:1, s:1, b:0),
% 3.07/3.51 c_SMT_Oz3mod [220, 2] (w:1, o:225, a:1, s:1, b:0),
% 3.07/3.51 c_Groups_Oabs__class_Oabs [221, 2] (w:1, o:226, a:1, s:1, b:0),
% 3.07/3.51 class_Groups_Ocancel__comm__monoid__add [223, 1] (w:1, o:181, a:1, s:
% 3.07/3.51 1, b:0),
% 3.07/3.51 tc_HOL_Obool [226, 0] (w:1, o:80, a:1, s:1, b:0),
% 3.07/3.51 t_a [228, 0] (w:1, o:98, a:1, s:1, b:0),
% 3.07/3.51 v_n [229, 0] (w:1, o:99, a:1, s:1, b:0),
% 3.07/3.51 v_p [230, 0] (w:1, o:100, a:1, s:1, b:0),
% 3.07/3.51 v_x [231, 0] (w:1, o:101, a:1, s:1, b:0),
% 3.07/3.51 alpha1 [232, 4] (w:1, o:306, a:1, s:1, b:1),
% 3.07/3.51 alpha2 [233, 4] (w:1, o:309, a:1, s:1, b:1),
% 3.07/3.51 alpha3 [234, 3] (w:1, o:260, a:1, s:1, b:1),
% 3.07/3.51 alpha4 [235, 3] (w:1, o:267, a:1, s:1, b:1),
% 3.07/3.51 alpha5 [236, 3] (w:1, o:277, a:1, s:1, b:1),
% 3.07/3.51 alpha6 [237, 3] (w:1, o:283, a:1, s:1, b:1),
% 3.07/3.51 alpha7 [238, 3] (w:1, o:284, a:1, s:1, b:1),
% 3.07/3.51 alpha8 [239, 2] (w:1, o:227, a:1, s:1, b:1),
% 3.07/3.51 alpha9 [240, 2] (w:1, o:228, a:1, s:1, b:1),
% 3.07/3.51 alpha10 [241, 2] (w:1, o:229, a:1, s:1, b:1),
% 3.07/3.51 alpha11 [242, 2] (w:1, o:230, a:1, s:1, b:1),
% 3.07/3.51 alpha12 [243, 2] (w:1, o:231, a:1, s:1, b:1),
% 3.07/3.51 alpha13 [244, 2] (w:1, o:232, a:1, s:1, b:1),
% 3.07/3.51 alpha14 [245, 2] (w:1, o:233, a:1, s:1, b:1),
% 3.07/3.51 alpha15 [246, 2] (w:1, o:234, a:1, s:1, b:1),
% 3.07/3.51 alpha16 [247, 2] (w:1, o:235, a:1, s:1, b:1),
% 3.07/3.51 alpha17 [248, 4] (w:1, o:307, a:1, s:1, b:1),
% 3.07/3.51 alpha18 [249, 3] (w:1, o:285, a:1, s:1, b:1),
% 3.07/3.51 alpha19 [250, 4] (w:1, o:308, a:1, s:1, b:1),
% 3.07/3.51 alpha20 [251, 4] (w:1, o:310, a:1, s:1, b:1),
% 3.07/3.51 alpha21 [252, 4] (w:1, o:311, a:1, s:1, b:1),
% 3.07/3.51 alpha22 [253, 3] (w:1, o:255, a:1, s:1, b:1),
% 3.07/3.51 alpha23 [254, 3] (w:1, o:256, a:1, s:1, b:1),
% 3.07/3.51 alpha24 [255, 3] (w:1, o:257, a:1, s:1, b:1),
% 3.07/3.51 alpha25 [256, 3] (w:1, o:258, a:1, s:1, b:1),
% 3.07/3.51 alpha26 [257, 2] (w:1, o:236, a:1, s:1, b:1),
% 3.07/3.51 alpha27 [258, 2] (w:1, o:237, a:1, s:1, b:1),
% 3.07/3.51 alpha28 [259, 2] (w:1, o:238, a:1, s:1, b:1),
% 3.07/3.51 alpha29 [260, 3] (w:1, o:259, a:1, s:1, b:1),
% 3.07/3.51 alpha30 [261, 3] (w:1, o:261, a:1, s:1, b:1),
% 3.07/3.51 alpha31 [262, 3] (w:1, o:262, a:1, s:1, b:1),
% 3.07/3.51 alpha32 [263, 4] (w:1, o:312, a:1, s:1, b:1),
% 3.07/3.51 alpha33 [264, 3] (w:1, o:263, a:1, s:1, b:1),
% 3.07/3.51 alpha34 [265, 4] (w:1, o:313, a:1, s:1, b:1),
% 3.07/3.51 alpha35 [266, 2] (w:1, o:239, a:1, s:1, b:1),
% 3.07/3.51 alpha36 [267, 3] (w:1, o:264, a:1, s:1, b:1),
% 3.07/3.51 alpha37 [268, 3] (w:1, o:265, a:1, s:1, b:1),
% 3.07/3.51 alpha38 [269, 4] (w:1, o:314, a:1, s:1, b:1),
% 3.07/3.51 alpha39 [270, 3] (w:1, o:266, a:1, s:1, b:1),
% 3.07/3.51 alpha40 [271, 3] (w:1, o:268, a:1, s:1, b:1),
% 3.07/3.51 alpha41 [272, 3] (w:1, o:269, a:1, s:1, b:1),
% 3.07/3.51 alpha42 [273, 4] (w:1, o:315, a:1, s:1, b:1),
% 3.07/3.51 alpha43 [274, 3] (w:1, o:270, a:1, s:1, b:1),
% 3.07/3.51 alpha44 [275, 3] (w:1, o:271, a:1, s:1, b:1),
% 3.07/3.51 alpha45 [276, 3] (w:1, o:272, a:1, s:1, b:1),
% 3.07/3.51 alpha46 [277, 3] (w:1, o:273, a:1, s:1, b:1),
% 3.07/3.51 alpha47 [278, 3] (w:1, o:274, a:1, s:1, b:1),
% 3.07/3.51 alpha48 [279, 3] (w:1, o:275, a:1, s:1, b:1),
% 3.07/3.51 alpha49 [280, 3] (w:1, o:276, a:1, s:1, b:1),
% 3.07/3.51 alpha50 [281, 4] (w:1, o:316, a:1, s:1, b:1),
% 3.07/3.51 alpha51 [282, 3] (w:1, o:278, a:1, s:1, b:1),
% 3.07/3.51 alpha52 [283, 3] (w:1, o:279, a:1, s:1, b:1),
% 3.07/3.51 alpha53 [284, 4] (w:1, o:317, a:1, s:1, b:1),
% 3.07/3.51 alpha54 [285, 3] (w:1, o:280, a:1, s:1, b:1),
% 3.07/3.51 alpha55 [286, 3] (w:1, o:281, a:1, s:1, b:1),
% 3.07/3.51 alpha56 [287, 2] (w:1, o:240, a:1, s:1, b:1),
% 20.80/21.18 alpha57 [288, 2] (w:1, o:241, a:1, s:1, b:1),
% 20.80/21.18 alpha58 [289, 3] (w:1, o:282, a:1, s:1, b:1),
% 20.80/21.18 skol1 [290, 2] (w:1, o:211, a:1, s:1, b:1),
% 20.80/21.18 skol2 [291, 2] (w:1, o:215, a:1, s:1, b:1),
% 20.80/21.18 skol3 [292, 3] (w:1, o:294, a:1, s:1, b:1),
% 20.80/21.18 skol4 [293, 3] (w:1, o:296, a:1, s:1, b:1),
% 20.80/21.18 skol5 [294, 2] (w:1, o:216, a:1, s:1, b:1),
% 20.80/21.18 skol6 [295, 3] (w:1, o:297, a:1, s:1, b:1),
% 20.80/21.18 skol7 [296, 3] (w:1, o:298, a:1, s:1, b:1),
% 20.80/21.18 skol8 [297, 2] (w:1, o:217, a:1, s:1, b:1),
% 20.80/21.18 skol9 [298, 1] (w:1, o:113, a:1, s:1, b:1),
% 20.80/21.18 skol10 [299, 2] (w:1, o:212, a:1, s:1, b:1),
% 20.80/21.18 skol11 [300, 2] (w:1, o:213, a:1, s:1, b:1),
% 20.80/21.18 skol12 [301, 3] (w:1, o:299, a:1, s:1, b:1),
% 20.80/21.18 skol13 [302, 3] (w:1, o:300, a:1, s:1, b:1),
% 20.80/21.18 skol14 [303, 3] (w:1, o:301, a:1, s:1, b:1),
% 20.80/21.18 skol15 [304, 3] (w:1, o:302, a:1, s:1, b:1),
% 20.80/21.18 skol16 [305, 2] (w:1, o:214, a:1, s:1, b:1),
% 20.80/21.18 skol17 [306, 3] (w:1, o:303, a:1, s:1, b:1),
% 20.80/21.18 skol18 [307, 4] (w:1, o:318, a:1, s:1, b:1),
% 20.80/21.18 skol19 [308, 3] (w:1, o:304, a:1, s:1, b:1),
% 20.80/21.18 skol20 [309, 2] (w:1, o:218, a:1, s:1, b:1),
% 20.80/21.18 skol21 [310, 3] (w:1, o:286, a:1, s:1, b:1),
% 20.80/21.18 skol22 [311, 2] (w:1, o:219, a:1, s:1, b:1),
% 20.80/21.18 skol23 [312, 3] (w:1, o:287, a:1, s:1, b:1),
% 20.80/21.18 skol24 [313, 3] (w:1, o:288, a:1, s:1, b:1),
% 20.80/21.18 skol25 [314, 3] (w:1, o:289, a:1, s:1, b:1),
% 20.80/21.18 skol26 [315, 3] (w:1, o:290, a:1, s:1, b:1),
% 20.80/21.18 skol27 [316, 3] (w:1, o:291, a:1, s:1, b:1),
% 20.80/21.18 skol28 [317, 3] (w:1, o:292, a:1, s:1, b:1),
% 20.80/21.18 skol29 [318, 3] (w:1, o:293, a:1, s:1, b:1),
% 20.80/21.18 skol30 [319, 3] (w:1, o:295, a:1, s:1, b:1).
% 20.80/21.18
% 20.80/21.18
% 20.80/21.18 Starting Search:
% 20.80/21.18
% 20.80/21.18 *** allocated 113905 integers for clauses
% 20.80/21.18 *** allocated 170857 integers for clauses
% 20.80/21.18 Resimplifying inuse:
% 20.80/21.18 Done
% 20.80/21.18
% 20.80/21.18
% 20.80/21.18 Intermediate Status:
% 20.80/21.18 Generated: 3087
% 20.80/21.18 Kept: 2022
% 20.80/21.18 Inuse: 70
% 20.80/21.18 Deleted: 1
% 20.80/21.18 Deletedinuse: 0
% 20.80/21.18
% 20.80/21.18 *** allocated 256285 integers for clauses
% 20.80/21.18 *** allocated 170857 integers for termspace/termends
% 20.80/21.18 Resimplifying inuse:
% 20.80/21.18 Done
% 20.80/21.18
% 20.80/21.18 *** allocated 384427 integers for clauses
% 20.80/21.18
% 20.80/21.18 Intermediate Status:
% 20.80/21.18 Generated: 8863
% 20.80/21.18 Kept: 4179
% 20.80/21.18 Inuse: 250
% 20.80/21.18 Deleted: 6
% 20.80/21.18 Deletedinuse: 0
% 20.80/21.18
% 20.80/21.18 Resimplifying inuse:
% 20.80/21.18 Done
% 20.80/21.18
% 20.80/21.18 *** allocated 256285 integers for termspace/termends
% 20.80/21.18 Resimplifying inuse:
% 20.80/21.18 Done
% 20.80/21.18
% 20.80/21.18
% 20.80/21.18 Intermediate Status:
% 20.80/21.18 Generated: 12593
% 20.80/21.18 Kept: 6190
% 20.80/21.18 Inuse: 314
% 20.80/21.18 Deleted: 7
% 20.80/21.18 Deletedinuse: 0
% 20.80/21.18
% 20.80/21.18 *** allocated 576640 integers for clauses
% 20.80/21.18 Resimplifying inuse:
% 20.80/21.18 Done
% 20.80/21.18
% 20.80/21.18 Resimplifying inuse:
% 20.80/21.18 Done
% 20.80/21.18
% 20.80/21.18
% 20.80/21.18 Intermediate Status:
% 20.80/21.18 Generated: 17142
% 20.80/21.18 Kept: 8679
% 20.80/21.18 Inuse: 358
% 20.80/21.18 Deleted: 8
% 20.80/21.18 Deletedinuse: 0
% 20.80/21.18
% 20.80/21.18 Resimplifying inuse:
% 20.80/21.18 Done
% 20.80/21.18
% 20.80/21.18 *** allocated 384427 integers for termspace/termends
% 20.80/21.18 Resimplifying inuse:
% 20.80/21.18 Done
% 20.80/21.18
% 20.80/21.18 *** allocated 864960 integers for clauses
% 20.80/21.18
% 20.80/21.18 Intermediate Status:
% 20.80/21.18 Generated: 20766
% 20.80/21.18 Kept: 10684
% 20.80/21.18 Inuse: 403
% 20.80/21.18 Deleted: 9
% 20.80/21.18 Deletedinuse: 0
% 20.80/21.18
% 20.80/21.18 Resimplifying inuse:
% 20.80/21.18 Done
% 20.80/21.18
% 20.80/21.18 Resimplifying inuse:
% 20.80/21.18 Done
% 20.80/21.18
% 20.80/21.18
% 20.80/21.18 Intermediate Status:
% 20.80/21.18 Generated: 26023
% 20.80/21.18 Kept: 12709
% 20.80/21.18 Inuse: 455
% 20.80/21.18 Deleted: 9
% 20.80/21.18 Deletedinuse: 0
% 20.80/21.18
% 20.80/21.18 Resimplifying inuse:
% 20.80/21.18 Done
% 20.80/21.18
% 20.80/21.18 Resimplifying inuse:
% 20.80/21.18 Done
% 20.80/21.18
% 20.80/21.18
% 20.80/21.18 Intermediate Status:
% 20.80/21.18 Generated: 33440
% 20.80/21.18 Kept: 15120
% 20.80/21.18 Inuse: 477
% 20.80/21.18 Deleted: 9
% 20.80/21.18 Deletedinuse: 0
% 20.80/21.18
% 20.80/21.18 Resimplifying inuse:
% 20.80/21.18 Done
% 20.80/21.18
% 20.80/21.18 Resimplifying inuse:
% 20.80/21.18 Done
% 20.80/21.18
% 20.80/21.18 *** allocated 576640 integers for termspace/termends
% 20.80/21.18 *** allocated 1297440 integers for clauses
% 20.80/21.18
% 20.80/21.18 Intermediate Status:
% 20.80/21.18 Generated: 38336
% 20.80/21.18 Kept: 17131
% 20.80/21.18 Inuse: 528
% 20.80/21.18 Deleted: 9
% 20.80/21.18 Deletedinuse: 0
% 20.80/21.18
% 20.80/21.18 Resimplifying inuse:
% 20.80/21.18 Done
% 20.80/21.18
% 20.80/21.18 Resimplifying inuse:
% 20.80/21.18 Done
% 20.80/21.18
% 20.80/21.18
% 20.80/21.18 Intermediate Status:
% 20.80/21.18 Generated: 44828
% 20.80/21.18 Kept: 19975
% 20.80/21.18 Inuse: 552
% 20.80/21.18 Deleted: 9
% 20.80/21.18 Deletedinuse: 0
% 20.80/21.18
% 20.80/21.18 Resimplifying inuse:
% 20.80/21.18 Done
% 20.80/21.18
% 20.80/21.18 Resimplifying clauses:
% 20.80/21.18 Done
% 20.80/21.18
% 20.80/21.18 Resimplifying inuse:
% 20.80/21.18 Done
% 20.80/21.18
% 20.80/21.18
% 20.80/21.18 Intermediate Status:
% 20.80/21.18 Generated: 61331
% 20.80/21.18 Kept: 23066
% 20.80/21.18 Inuse: 577
% 20.80/21.18 Deleted: 189
% 20.80/21.18 Deletedinuse: 0
% 20.80/21.18
% 20.80/21.18 Resimplifying inuse:
% 20.80/21.18 Done
% 20.80/21.18
% 20.80/21.18 Resimplifying inuse:
% 20.80/21.18 Done
% 20.80/21.18
% 20.80/21.18 *** allocated 864960 integers for termspace/termends
% 20.80/21.18
% 20.80/21.18 Intermediate Status:
% 20.80/21.18 Generated: 68476
% 20.80/21.18 Kept: 25066
% 20.80/21.18 Inuse: 595
% 20.80/21.18 Deleted: 189
% 20.80/21.18 Deletedinuse: 0
% 20.80/21.18
% 20.80/21.18 Resimplifying inuse:
% 20.80/21.18 Done
% 20.80/21.18
% 20.80/21.18 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49 *** allocated 1946160 integers for clauses
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 77122
% 75.13/75.49 Kept: 28138
% 75.13/75.49 Inuse: 632
% 75.13/75.49 Deleted: 189
% 75.13/75.49 Deletedinuse: 0
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 85077
% 75.13/75.49 Kept: 30290
% 75.13/75.49 Inuse: 662
% 75.13/75.49 Deleted: 189
% 75.13/75.49 Deletedinuse: 0
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 103778
% 75.13/75.49 Kept: 32313
% 75.13/75.49 Inuse: 668
% 75.13/75.49 Deleted: 189
% 75.13/75.49 Deletedinuse: 0
% 75.13/75.49
% 75.13/75.49 *** allocated 1297440 integers for termspace/termends
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 114718
% 75.13/75.49 Kept: 35030
% 75.13/75.49 Inuse: 697
% 75.13/75.49 Deleted: 189
% 75.13/75.49 Deletedinuse: 0
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 122494
% 75.13/75.49 Kept: 37041
% 75.13/75.49 Inuse: 723
% 75.13/75.49 Deleted: 189
% 75.13/75.49 Deletedinuse: 0
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 132632
% 75.13/75.49 Kept: 39096
% 75.13/75.49 Inuse: 752
% 75.13/75.49 Deleted: 189
% 75.13/75.49 Deletedinuse: 0
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49 *** allocated 2919240 integers for clauses
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49 Resimplifying clauses:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 140374
% 75.13/75.49 Kept: 41449
% 75.13/75.49 Inuse: 762
% 75.13/75.49 Deleted: 323
% 75.13/75.49 Deletedinuse: 0
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 159739
% 75.13/75.49 Kept: 44861
% 75.13/75.49 Inuse: 772
% 75.13/75.49 Deleted: 323
% 75.13/75.49 Deletedinuse: 0
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49 *** allocated 1946160 integers for termspace/termends
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 167217
% 75.13/75.49 Kept: 46934
% 75.13/75.49 Inuse: 812
% 75.13/75.49 Deleted: 323
% 75.13/75.49 Deletedinuse: 0
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 177564
% 75.13/75.49 Kept: 51603
% 75.13/75.49 Inuse: 842
% 75.13/75.49 Deleted: 323
% 75.13/75.49 Deletedinuse: 0
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 188897
% 75.13/75.49 Kept: 54734
% 75.13/75.49 Inuse: 876
% 75.13/75.49 Deleted: 324
% 75.13/75.49 Deletedinuse: 0
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 196848
% 75.13/75.49 Kept: 56778
% 75.13/75.49 Inuse: 886
% 75.13/75.49 Deleted: 327
% 75.13/75.49 Deletedinuse: 3
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 210549
% 75.13/75.49 Kept: 59996
% 75.13/75.49 Inuse: 916
% 75.13/75.49 Deleted: 327
% 75.13/75.49 Deletedinuse: 3
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 214186
% 75.13/75.49 Kept: 62139
% 75.13/75.49 Inuse: 921
% 75.13/75.49 Deleted: 327
% 75.13/75.49 Deletedinuse: 3
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49 Resimplifying clauses:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49 *** allocated 4378860 integers for clauses
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 226510
% 75.13/75.49 Kept: 65149
% 75.13/75.49 Inuse: 951
% 75.13/75.49 Deleted: 3719
% 75.13/75.49 Deletedinuse: 3
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 236311
% 75.13/75.49 Kept: 67635
% 75.13/75.49 Inuse: 961
% 75.13/75.49 Deleted: 3719
% 75.13/75.49 Deletedinuse: 3
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 246269
% 75.13/75.49 Kept: 69636
% 75.13/75.49 Inuse: 1008
% 75.13/75.49 Deleted: 3719
% 75.13/75.49 Deletedinuse: 3
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 263046
% 75.13/75.49 Kept: 72138
% 75.13/75.49 Inuse: 1021
% 75.13/75.49 Deleted: 3722
% 75.13/75.49 Deletedinuse: 6
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 278816
% 75.13/75.49 Kept: 74352
% 75.13/75.49 Inuse: 1031
% 75.13/75.49 Deleted: 3722
% 75.13/75.49 Deletedinuse: 6
% 75.13/75.49
% 75.13/75.49 *** allocated 2919240 integers for termspace/termends
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 307003
% 75.13/75.49 Kept: 79096
% 75.13/75.49 Inuse: 1065
% 75.13/75.49 Deleted: 3724
% 75.13/75.49 Deletedinuse: 7
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 320729
% 75.13/75.49 Kept: 83402
% 75.13/75.49 Inuse: 1094
% 75.13/75.49 Deleted: 3731
% 75.13/75.49 Deletedinuse: 8
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49 Resimplifying clauses:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 325566
% 75.13/75.49 Kept: 85920
% 75.13/75.49 Inuse: 1099
% 75.13/75.49 Deleted: 4062
% 75.13/75.49 Deletedinuse: 8
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49
% 75.13/75.49 Intermediate Status:
% 75.13/75.49 Generated: 330552
% 75.13/75.49 Kept: 88451
% 75.13/75.49 Inuse: 1104
% 75.13/75.49 Deleted: 4062
% 75.13/75.49 Deletedinuse: 8
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 75.13/75.49
% 75.13/75.49 Resimplifying inuse:
% 75.13/75.49 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 358904
% 162.28/162.73 Kept: 91531
% 162.28/162.73 Inuse: 1119
% 162.28/162.73 Deleted: 4064
% 162.28/162.73 Deletedinuse: 10
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 385957
% 162.28/162.73 Kept: 94131
% 162.28/162.73 Inuse: 1129
% 162.28/162.73 Deleted: 4064
% 162.28/162.73 Deletedinuse: 10
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 410465
% 162.28/162.73 Kept: 97701
% 162.28/162.73 Inuse: 1149
% 162.28/162.73 Deleted: 4064
% 162.28/162.73 Deletedinuse: 10
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73 *** allocated 6568290 integers for clauses
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 422240
% 162.28/162.73 Kept: 99850
% 162.28/162.73 Inuse: 1178
% 162.28/162.73 Deleted: 4065
% 162.28/162.73 Deletedinuse: 10
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 430518
% 162.28/162.73 Kept: 102834
% 162.28/162.73 Inuse: 1188
% 162.28/162.73 Deleted: 4065
% 162.28/162.73 Deletedinuse: 10
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 436468
% 162.28/162.73 Kept: 105372
% 162.28/162.73 Inuse: 1193
% 162.28/162.73 Deleted: 4065
% 162.28/162.73 Deletedinuse: 10
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73 Resimplifying clauses:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 448355
% 162.28/162.73 Kept: 107723
% 162.28/162.73 Inuse: 1218
% 162.28/162.73 Deleted: 4304
% 162.28/162.73 Deletedinuse: 11
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73 *** allocated 4378860 integers for termspace/termends
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 457665
% 162.28/162.73 Kept: 109936
% 162.28/162.73 Inuse: 1238
% 162.28/162.73 Deleted: 4304
% 162.28/162.73 Deletedinuse: 11
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 465726
% 162.28/162.73 Kept: 111956
% 162.28/162.73 Inuse: 1258
% 162.28/162.73 Deleted: 4304
% 162.28/162.73 Deletedinuse: 11
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 474483
% 162.28/162.73 Kept: 114110
% 162.28/162.73 Inuse: 1278
% 162.28/162.73 Deleted: 4304
% 162.28/162.73 Deletedinuse: 11
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 481865
% 162.28/162.73 Kept: 116250
% 162.28/162.73 Inuse: 1312
% 162.28/162.73 Deleted: 4305
% 162.28/162.73 Deletedinuse: 11
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 488077
% 162.28/162.73 Kept: 118331
% 162.28/162.73 Inuse: 1342
% 162.28/162.73 Deleted: 4305
% 162.28/162.73 Deletedinuse: 11
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 502011
% 162.28/162.73 Kept: 121940
% 162.28/162.73 Inuse: 1381
% 162.28/162.73 Deleted: 4306
% 162.28/162.73 Deletedinuse: 11
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 513851
% 162.28/162.73 Kept: 124389
% 162.28/162.73 Inuse: 1391
% 162.28/162.73 Deleted: 4306
% 162.28/162.73 Deletedinuse: 11
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 523081
% 162.28/162.73 Kept: 126684
% 162.28/162.73 Inuse: 1406
% 162.28/162.73 Deleted: 4306
% 162.28/162.73 Deletedinuse: 11
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73 Resimplifying clauses:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 532506
% 162.28/162.73 Kept: 130022
% 162.28/162.73 Inuse: 1421
% 162.28/162.73 Deleted: 4642
% 162.28/162.73 Deletedinuse: 11
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 542104
% 162.28/162.73 Kept: 132049
% 162.28/162.73 Inuse: 1447
% 162.28/162.73 Deleted: 4642
% 162.28/162.73 Deletedinuse: 11
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 557492
% 162.28/162.73 Kept: 135481
% 162.28/162.73 Inuse: 1466
% 162.28/162.73 Deleted: 4642
% 162.28/162.73 Deletedinuse: 11
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 567266
% 162.28/162.73 Kept: 137545
% 162.28/162.73 Inuse: 1474
% 162.28/162.73 Deleted: 4642
% 162.28/162.73 Deletedinuse: 11
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 577349
% 162.28/162.73 Kept: 139545
% 162.28/162.73 Inuse: 1488
% 162.28/162.73 Deleted: 4642
% 162.28/162.73 Deletedinuse: 11
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 587615
% 162.28/162.73 Kept: 141581
% 162.28/162.73 Inuse: 1506
% 162.28/162.73 Deleted: 4642
% 162.28/162.73 Deletedinuse: 11
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 596839
% 162.28/162.73 Kept: 143702
% 162.28/162.73 Inuse: 1516
% 162.28/162.73 Deleted: 4643
% 162.28/162.73 Deletedinuse: 12
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 606657
% 162.28/162.73 Kept: 145706
% 162.28/162.73 Inuse: 1535
% 162.28/162.73 Deleted: 4643
% 162.28/162.73 Deletedinuse: 12
% 162.28/162.73
% 162.28/162.73 Resimplifying inuse:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73 Resimplifying clauses:
% 162.28/162.73 Done
% 162.28/162.73
% 162.28/162.73
% 162.28/162.73 Intermediate Status:
% 162.28/162.73 Generated: 624694
% 162.28/162.73 Kept: 149074
% 162.28/162.73 Inuse: 1541
% 162.28/162.73 Deleted: 4Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------