TSTP Solution File: SWW290+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW290+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.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 23:21:52 EDT 2022
% Result : Timeout 300.04s 300.47s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW290+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Mon Jun 6 03:42:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.97/1.61 *** allocated 10000 integers for termspace/termends
% 0.97/1.61 *** allocated 10000 integers for clauses
% 0.97/1.61 *** allocated 10000 integers for justifications
% 0.97/1.61 *** allocated 15000 integers for termspace/termends
% 0.97/1.61 *** allocated 22500 integers for termspace/termends
% 0.97/1.61 *** allocated 33750 integers for termspace/termends
% 0.97/1.61 Bliksem 1.12
% 0.97/1.61
% 0.97/1.61
% 0.97/1.61 Automatic Strategy Selection
% 0.97/1.61
% 0.97/1.61 *** allocated 50625 integers for termspace/termends
% 0.97/1.61 *** allocated 75937 integers for termspace/termends
% 0.97/1.61 *** allocated 113905 integers for termspace/termends
% 0.97/1.61
% 0.97/1.61 Clauses:
% 0.97/1.61
% 0.97/1.61 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.97/1.61 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ), v_p
% 0.97/1.61 , v_q ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 0.97/1.61 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.97/1.61 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 0.97/1.61 Y ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.61 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.61 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.97/1.61 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 0.97/1.61 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 0.97/1.61 .
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.61 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 0.97/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 0.97/1.61 ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.97/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.97/1.61 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.97/1.61 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.97/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y
% 0.97/1.61 , X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex
% 0.97/1.61 ), Y, c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), X ) ) }.
% 0.97/1.61 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.97/1.61 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.97/1.61 tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.97/1.61 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.97/1.61 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 0.97/1.61 X, T, Z ), Y ) }.
% 0.97/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.97/1.61 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 0.97/1.61 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.97/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.97/1.61 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 0.97/1.61 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.97/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha1( X
% 0.97/1.61 , Y, T ) }.
% 0.97/1.61 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.97/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha26( X
% 0.97/1.61 , Y, Z, T ) }.
% 0.97/1.61 { ! class_Fields_Ofield( X ), ! alpha1( X, Y, T ), ! alpha26( X, Y, Z, T )
% 0.97/1.61 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 0.97/1.61 ( X, T, Z ), Y ) }.
% 0.97/1.61 { ! alpha26( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.97/1.61 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha26( X, Y, Z, T ) }.
% 0.97/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha26( X
% 0.97/1.61 , Y, Z, T ) }.
% 0.97/1.61 { ! alpha1( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.61 { Z = c_Groups_Ozero__class_Ozero( X ), alpha1( X, Y, Z ) }.
% 0.97/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha1( X
% 0.97/1.61 , Y, Z ) }.
% 0.97/1.61 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.97/1.61 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.97/1.61 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.97/1.61 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.97/1.61 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.97/1.61 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.97/1.61 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.61 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.97/1.61 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.97/1.61 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.97/1.61 }.
% 0.97/1.61 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.97/1.61 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.97/1.61 }.
% 0.97/1.61 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.97/1.61 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.97/1.61 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.97/1.61 }.
% 0.97/1.61 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.97/1.61 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.97/1.61 }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 0.97/1.61 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.97/1.61 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.61 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.61 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.61 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.61 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.61 ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.61 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.97/1.61 Z, T ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.97/1.61 ) }.
% 0.97/1.61 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.61 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.61 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.61 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.97/1.61 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.97/1.61 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.97/1.61 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.97/1.61 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.97/1.61 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.97/1.61 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.97/1.61 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 0.97/1.61 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 0.97/1.61 .
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.61 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.97/1.61 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 0.97/1.61 .
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.97/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.97/1.61 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 0.97/1.61 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.61 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.97/1.61 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.97/1.61 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.97/1.61 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.97/1.61 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.61 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.61 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.61 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.97/1.61 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.97/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.97/1.61 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.97/1.61 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.97/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.61 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.61 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.61 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.61 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.97/1.61 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.97/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.61 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.61 ), U = Z, T = Y }.
% 0.97/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.61 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.61 ) }.
% 0.97/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.61 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.61 ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.97/1.61 ) ), Z ) }.
% 0.97/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.61 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.61 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.61 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.61 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.61 ) }.
% 0.97/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.61 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.61 ), ! U = T }.
% 0.97/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.61 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.61 ), ! Z = Y }.
% 0.97/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.61 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.61 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.61 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.97/1.62 ) ), T ), Y ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.62 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.62 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.97/1.62 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.97/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.97/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.62 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 0.97/1.62 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.97/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.97/1.62 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 0.97/1.62 c_Polynomial_OpCons( X, T,
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), !
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.97/1.62 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.97/1.62 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.97/1.62 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.97/1.62 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.97/1.62 hAPP( Z, skol2( U, W, Z ) ) ) }.
% 0.97/1.62 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.97/1.62 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol2( X
% 0.97/1.62 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.97/1.62 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 0.97/1.62 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol17( X,
% 0.97/1.62 Y, Z ) ) ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.97/1.62 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.97/1.62 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.62 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.62 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.62 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.62 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.62 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.97/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.62 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.62 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.97/1.62 tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.97/1.62 ) ), X ) = hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.97/1.62 ), X ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.62 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.97/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.97/1.62 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.97/1.62 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.97/1.62 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.97/1.62 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.97/1.62 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.62 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.97/1.62 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.97/1.62 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.97/1.62 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.62 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.97/1.62 , Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.97/1.62 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.97/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.97/1.62 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.97/1.62 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.97/1.62 ) }.
% 0.97/1.62 { c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) = hAPP(
% 0.97/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) ), X ) }.
% 0.97/1.62 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.97/1.62 ), X ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.62 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), X ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.97/1.62 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.97/1.62 tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 0.97/1.62 Y ) ), X ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.62 { Y = hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.97/1.62 tc_Complex_Ocomplex, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 0.97/1.62 ( tc_Complex_Ocomplex ) ) ) ), X ) }.
% 0.97/1.62 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.97/1.62 tc_Complex_Ocomplex, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 0.97/1.62 ( tc_Complex_Ocomplex ) ) ) ), X ) = Y }.
% 0.97/1.62 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.97/1.62 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.97/1.62 ), Y ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.97/1.62 tc_Complex_Ocomplex ) ) ) ), X ) = hAPP( c_Polynomial_Opoly(
% 0.97/1.62 tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.97/1.62 tc_Complex_Ocomplex ) ) ), X ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 0.97/1.62 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.62 , Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.97/1.62 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 Y, T ), Z = Y }.
% 0.97/1.62 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 T, Y ), Z = Y }.
% 0.97/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 T, Y ), Z = Y }.
% 0.97/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 Y, Z ), T = Y }.
% 0.97/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 Y, Z ) }.
% 0.97/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 T, Y ), Z = Y }.
% 0.97/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 T, Y ) }.
% 0.97/1.62 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 0.97/1.62 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 0.97/1.62 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 0.97/1.62 , Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.97/1.62 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.97/1.62 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.62 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { X = hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.97/1.62 tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 0.97/1.62 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.97/1.62 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.97/1.62 tc_Complex_Ocomplex ) ) ) ) ), X ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.97/1.62 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.97/1.62 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.97/1.62 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 0.97/1.62 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 0.97/1.62 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.97/1.62 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.97/1.62 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.97/1.62 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.97/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.62 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.97/1.62 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.97/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.97/1.62 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 0.97/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.97/1.62 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 0.97/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.97/1.62 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 0.97/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.97/1.62 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.97/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.97/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.62 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.62 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.62 = Y }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.62 = Y }.
% 0.97/1.62 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.62 = Y }.
% 0.97/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.62 = Y }.
% 0.97/1.62 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.62 = Y }.
% 0.97/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.62 = Y }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.97/1.62 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 0.97/1.62 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.97/1.62 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 0.97/1.62 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 0.97/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 0.97/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.97/1.62 , c_Polynomial_Opdivmod__rel( X, c_Polynomial_Osmult( X, W, U ), T,
% 0.97/1.62 c_Polynomial_Osmult( X, W, Z ), c_Polynomial_Osmult( X, W, Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.62 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.62 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.62 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.62 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.97/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.97/1.62 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.97/1.62 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.97/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 0.97/1.62 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.97/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.97/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.97/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.97/1.62 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.97/1.62 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 0.97/1.62 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), !
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 0.97/1.62 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.97/1.62 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.97/1.62 ), Y ) }.
% 0.97/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), X ) = X }.
% 0.97/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ) ) = X }.
% 0.97/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.62 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X, Y ), Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.62 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.62 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.97/1.62 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.97/1.62 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.62 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X, Y ), Z = Y }.
% 0.97/1.62 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X, Y ) }.
% 0.97/1.62 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.62 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.62 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.62 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.62 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.62 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.97/1.62 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.97/1.62 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.97/1.62 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.97/1.62 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.97/1.62 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.97/1.62 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.62 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.62 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.62 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.62 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.62 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.62 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.62 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.62 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.62 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.62 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.97/1.62 ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.97/1.62 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.97/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.97/1.62 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.97/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol3( X, Y ) ) }.
% 0.97/1.62 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 = Y }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.62 , Y ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.62 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.62 = Y }.
% 0.97/1.62 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X, Y ) ) }.
% 0.97/1.62 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.62 ) ), Y ) }.
% 0.97/1.62 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.62 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X, Y ) ) }.
% 0.97/1.62 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.62 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.97/1.62 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.97/1.62 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.62 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.62 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 Z, Y ) ) = Y }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.97/1.62 Y ) ) = Y }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.97/1.62 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.97/1.62 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 0.97/1.62 , Z, Y ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.97/1.62 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.97/1.62 , Y ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.97/1.62 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.62 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.62 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.62 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.62 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.62 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.62 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.62 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.62 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.62 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.97/1.62 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.97/1.62 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.62 Z ) = Y }.
% 0.97/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.62 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.97/1.62 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X, Y ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.62 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.97/1.62 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.62 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.97/1.62 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.62 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.97/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.62 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha2( X, Y
% 0.97/1.62 , Z ), alpha27( X, Y, Z ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha27( X, Y, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), alpha27( X, Y, Z ) }.
% 0.97/1.62 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.62 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y ), alpha2( X, Y, Z ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ) ), alpha3( X, Y, Z ), alpha28( X, Y, Z ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha28( X, Y, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ) ) }.
% 0.97/1.62 { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ), Y ), alpha28( X, Y, Z ) }.
% 0.97/1.62 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.62 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), alpha3( X, Y, Z ) }.
% 0.97/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 Z, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 Y, Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.97/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.62 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.97/1.62 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.97/1.62 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.97/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.97/1.62 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.97/1.62 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.97/1.62 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.62 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.97/1.62 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.97/1.62 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.97/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.97/1.62 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.62 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.97/1.62 .
% 0.97/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.97/1.62 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.62 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.97/1.62 .
% 0.97/1.62 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.97/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.97/1.62 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X, Z ) }.
% 0.97/1.62 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.62 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.97/1.62 , Y ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.97/1.62 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 0.97/1.62 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.97/1.62 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.97/1.62 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 0.97/1.62 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 0.97/1.62 X, Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.97/1.62 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.97/1.62 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 0.97/1.62 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.62 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 0.97/1.62 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.62 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.97/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.97/1.62 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.97/1.62 tc_Nat_Onat ) }.
% 0.97/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.97/1.62 tc_Nat_Onat ) }.
% 0.97/1.62 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.97/1.62 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.62 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.62 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.97/1.62 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.62 , Y ), X ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.97/1.62 tc_Nat_Onat ) ) = Y }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.97/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.62 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.62 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.62 ( X, Z, Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! Z = Y }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.62 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.97/1.62 tc_Nat_Onat, Y, Z ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 0.97/1.62 , Z ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 0.97/1.62 Z, Y ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.97/1.62 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.97/1.62 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.62 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.97/1.62 tc_Nat_Onat, Y, Z ) }.
% 0.97/1.62 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.97/1.62 tc_Nat_Onat, Y, Z ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.97/1.62 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.97/1.62 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.97/1.62 { ! alpha4( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! alpha4( X, Y ), ! Y = X }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha4( X, Y ) }
% 0.97/1.62 .
% 0.97/1.62 { ! alpha4( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! alpha4( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Nat_Onat, X, Y ), alpha4( X, Y ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha5( X, Y ), Y = X }
% 0.97/1.62 .
% 0.97/1.62 { ! alpha5( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! alpha5( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! alpha5( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Nat_Onat, X, Y ), alpha5( X, Y ) }.
% 0.97/1.62 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.62 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.97/1.62 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.97/1.62 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.97/1.62 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.97/1.62 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.62 Y ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! Z = Y }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.62 Z ), ! Z = Y }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.62 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! Z = Y }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! Z = Y }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! Y = Z }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.97/1.62 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 0.97/1.62 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 0.97/1.62 c_Polynomial_Ocoeff( X, Y ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 0.97/1.62 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol4( X
% 0.97/1.62 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol4( X, Y, Z ) ), Z = Y
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.97/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.62 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.62 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.62 tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.62 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, T, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.62 , Y, Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.62 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, Z, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.62 , T, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.62 , Y, T ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.62 , T, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.62 , T ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.97/1.62 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, Z, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.62 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, Z, Y ) }.
% 0.97/1.62 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.62 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.97/1.62 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.97/1.62 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X, Y ), Z ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.62 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.97/1.62 ( X, Z ), Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.62 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.62 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), X ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.97/1.62 ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.97/1.62 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.97/1.62 ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.97/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.97/1.62 ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.97/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), Z ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.62 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.62 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.62 Y ), X ) ) }.
% 0.97/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.97/1.62 .
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.97/1.62 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.97/1.62 .
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.97/1.62 .
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.97/1.62 .
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.97/1.62 , X ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.97/1.62 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.97/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 0.97/1.62 ( X ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.62 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.62 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.62 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.62 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.62 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha6( X, Y, Z, T ),
% 0.97/1.62 alpha29( X, Y, Z, T ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha29( X, Y, Z, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.62 { ! alpha29( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! alpha29( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.62 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha29( X, Y, Z, T ) }.
% 0.97/1.62 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.97/1.62 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.97/1.62 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha6( X, Y, Z, T ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha7( X, Y, Z, T ),
% 0.97/1.62 alpha30( X, Y, Z, T ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha7( X, Y, Z, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha30( X, Y, Z, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! alpha30( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! alpha30( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.62 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha30( X, Y, Z, T ) }.
% 0.97/1.62 { ! alpha7( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.62 { ! alpha7( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.62 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha7( X, Y, Z, T ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.62 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.97/1.62 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.62 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.62 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.62 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.62 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.97/1.62 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.62 , Y, T ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.62 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.62 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.62 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 , Y ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.62 , Y ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.62 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ) ) = Z }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.62 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 0.97/1.62 ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.62 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.62 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 0.97/1.62 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.62 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.62 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.62 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.62 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.62 hAPP( Y, U ) ) }.
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.97/1.62 ( Z, skol5( X, Y, Z ) ), hAPP( Y, skol5( X, Y, Z ) ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.62 ( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.62 ( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.62 hAPP( Y, U ) ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.62 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.97/1.62 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.62 hAPP( Y, U ) ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.62 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.97/1.62 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.97/1.62 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.62 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.97/1.62 .
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.97/1.62 tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.62 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.97/1.62 X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.97/1.62 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.62 ( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.97/1.62 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.62 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.62 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.97/1.62 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.97/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.62 { alpha61( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.97/1.62 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.97/1.62 { alpha61( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.97/1.62 ( X, Y ), Z ) ) }.
% 0.97/1.62 { ! alpha61( X, Y, Z ), alpha62( X, Y, Z ), Z = Y }.
% 0.97/1.62 { ! alpha61( X, Y, Z ), alpha62( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! alpha62( X, Y, Z ), alpha61( X, Y, Z ) }.
% 0.97/1.62 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha61( X, Y, Z ) }.
% 0.97/1.62 { ! alpha62( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.97/1.62 }.
% 0.97/1.62 { ! alpha62( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.97/1.62 X, Y ), Z ) ), alpha62( X, Y, Z ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.97/1.62 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.97/1.62 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.97/1.62 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.97/1.62 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.97/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.97/1.62 , Z ), X ) ), T ) ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Int_Oint, U, T ) ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.97/1.62 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.97/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.97/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.97/1.62 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 0.97/1.62 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 0.97/1.62 ) ) }.
% 0.97/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 0.97/1.62 tc_Int_Oint, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.97/1.62 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.97/1.62 ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.97/1.62 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.97/1.62 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.62 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ) }.
% 0.97/1.62 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.62 = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.62 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.97/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.97/1.62 tc_Nat_Onat ) ) = Y }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.97/1.62 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.62 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.62 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.62 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.62 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ) }.
% 0.97/1.62 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.62 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.62 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.97/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.62 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.97/1.62 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.97/1.62 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.97/1.62 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.62 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.97/1.62 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.97/1.62 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.97/1.62 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.97/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.97/1.62 ), T ), U ), Y ) }.
% 0.97/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.97/1.62 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.97/1.62 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.97/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.26/1.62 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.26/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.26/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.26/1.62 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.26/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.26/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.26/1.62 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.26/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.26/1.62 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.62 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.26/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.26/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.62 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.26/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.26/1.62 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.26/1.62 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.26/1.62 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.26/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.26/1.62 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 1.26/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.26/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 1.26/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.26/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 1.26/1.62 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.62 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.62 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.62 tc_Nat_Onat ), Y ) }.
% 1.26/1.62 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.62 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.26/1.62 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 1.26/1.62 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.26/1.62 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.26/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.26/1.62 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.26/1.62 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.62 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.26/1.62 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.26/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.26/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.26/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.26/1.62 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.26/1.62 Y ) ) ), Y ) }.
% 1.26/1.62 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.62 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.26/1.62 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.26/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.26/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.26/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.26/1.62 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.26/1.62 Y ) ) ), Y ) }.
% 1.26/1.62 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.26/1.62 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.26/1.62 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.26/1.62 X ) ) }.
% 1.26/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 1.26/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.62 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 1.26/1.62 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.26/1.62 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.26/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.26/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.62 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.26/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.26/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.62 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.26/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.26/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.26/1.62 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 1.26/1.62 }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.26/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.26/1.62 tc_Int_Oint ) ) ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.26/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.26/1.62 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 1.26/1.62 = X }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.26/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.26/1.62 tc_Int_Oint ) ) ) }.
% 1.26/1.62 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.26/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.26/1.62 tc_Int_Oint ) ) ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.26/1.62 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 1.26/1.62 }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.26/1.62 tc_Int_Oint ) ), X ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.26/1.62 tc_Int_Oint ) ), X ) }.
% 1.26/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.62 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 1.26/1.62 ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.26/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 1.26/1.62 ( tc_Int_Oint, Y, X ), X = Y }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.62 tc_Int_Oint ), X ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.62 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 1.26/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.62 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.26/1.62 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 1.26/1.62 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 1.26/1.62 .
% 1.26/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 1.26/1.62 .
% 1.26/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.26/1.62 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.26/1.62 X ) ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.62 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 1.26/1.62 }.
% 1.26/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.26/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.62 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.26/1.62 .
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.26/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 1.26/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.62 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.26/1.62 .
% 1.26/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.26/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.26/1.62 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.26/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 1.26/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.26/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.62 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.26/1.62 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 1.26/1.62 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.62 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 1.26/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 1.26/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.62 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 1.26/1.62 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.26/1.62 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.26/1.62 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 1.26/1.62 ) ) }.
% 1.26/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.26/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.26/1.62 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.62 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.26/1.62 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.26/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.26/1.62 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.26/1.62 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 1.26/1.62 .
% 1.26/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 1.26/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.26/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.26/1.62 ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.62 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.26/1.62 , c_Nat_OSuc( X ) ) }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.26/1.62 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 1.26/1.62 }.
% 1.26/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.26/1.63 c_Nat_OSuc( X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.26/1.63 ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.26/1.63 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 1.26/1.63 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.26/1.63 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 1.26/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Int_Oint ), X ) = X }.
% 1.26/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Int_Oint ) ) = X }.
% 1.26/1.63 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.26/1.63 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.26/1.63 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 1.26/1.63 { ! c_Nat_OSuc( X ) = X }.
% 1.26/1.63 { ! X = c_Nat_OSuc( X ) }.
% 1.26/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.26/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.26/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 1.26/1.63 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 1.26/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.26/1.63 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 1.26/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.63 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 1.26/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.26/1.63 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 1.26/1.63 .
% 1.26/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.63 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.26/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.26/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 1.26/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.26/1.63 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.26/1.63 ( tc_Int_Oint ) }.
% 1.26/1.63 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.26/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.26/1.63 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.26/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.26/1.63 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.63 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.26/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.26/1.63 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.26/1.63 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.26/1.63 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol6( X ) ) }.
% 1.26/1.63 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 1.26/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.63 { ! alpha8( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.26/1.63 c_Nat_OSuc( X ) ) }.
% 1.26/1.63 { ! alpha8( X, Y ), Y = c_Nat_OSuc( skol7( Z, Y ) ) }.
% 1.26/1.63 { ! alpha8( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol7( X, Y
% 1.26/1.63 ), X ) }.
% 1.26/1.63 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.26/1.63 ), alpha8( X, Y ) }.
% 1.26/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.63 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.26/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.26/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha9( X, Y ), alpha31( X
% 1.26/1.63 , Y ) }.
% 1.26/1.63 { ! alpha9( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.26/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.63 { ! alpha31( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.26/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.63 { ! alpha31( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! alpha31( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ) ) }.
% 1.26/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha31( X, Y ) }.
% 1.26/1.63 { ! alpha9( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ) ) }.
% 1.26/1.63 { ! alpha9( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha9( X, Y ) }.
% 1.26/1.63 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha10( X, Y ),
% 1.26/1.63 alpha32( X, Y ) }.
% 1.26/1.63 { ! alpha10( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.26/1.63 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { ! alpha32( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.26/1.63 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { ! alpha32( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! alpha32( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ) ) }.
% 1.26/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha32( X, Y ) }.
% 1.26/1.63 { ! alpha10( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ) ) }.
% 1.26/1.63 { ! alpha10( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha10( X, Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 1.26/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 1.26/1.63 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 1.26/1.63 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.63 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.26/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol8( X, Y ) ) ) }.
% 1.26/1.63 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 1.26/1.63 .
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.26/1.63 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.26/1.63 ), X ) ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 1.26/1.63 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 1.26/1.63 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.26/1.63 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.26/1.63 ), X ) ) }.
% 1.26/1.63 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.26/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.26/1.63 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.26/1.63 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 1.26/1.63 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 X ), Y ), Z = Y }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 1.26/1.63 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.26/1.63 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.26/1.63 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 1.26/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 1.26/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.26/1.63 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.26/1.63 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.26/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 1.26/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 1.26/1.63 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.63 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 1.26/1.63 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.63 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 1.26/1.63 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 1.26/1.63 c_Groups_Oone__class_Oone( X ) ) }.
% 1.26/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.26/1.63 tc_Nat_Onat, Z, X ) }.
% 1.26/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.26/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 1.26/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.26/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.26/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.26/1.63 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 1.26/1.63 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 1.26/1.63 ) }.
% 1.26/1.63 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ) ) }.
% 1.26/1.63 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.26/1.63 tc_Nat_Onat ), X ) }.
% 1.26/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.26/1.63 tc_Int_Oint, Z, X ) }.
% 1.26/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.26/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 1.26/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.26/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.26/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.26/1.63 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 1.26/1.63 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 1.26/1.63 ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.26/1.63 ( tc_Int_Oint ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.26/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.26/1.63 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.26/1.63 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.26/1.63 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.26/1.63 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 1.26/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.26/1.63 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.26/1.63 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.26/1.63 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ), Y ) }.
% 1.26/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.26/1.63 ), X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Int_Oint ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.26/1.63 tc_Int_Oint ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Int_Oint, X, Y ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol9( X, Y ) ) }.
% 1.26/1.63 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.26/1.63 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.26/1.63 alpha11( X, Y, Z ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.26/1.63 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), ! alpha11( X, Y, Z ),
% 1.26/1.63 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.26/1.63 { ! alpha11( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.26/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.26/1.63 alpha11( X, Y, Z ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.26/1.63 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.26/1.63 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.26/1.63 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 1.26/1.63 .
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.26/1.63 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol10( Z, Y ) ) ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 1.26/1.63 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 1.26/1.63 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Int_Oint, skol10( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 1.26/1.63 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 1.26/1.63 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 1.26/1.63 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 1.26/1.63 ) ) }.
% 1.26/1.63 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.26/1.63 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol11( Z, Y
% 1.26/1.63 ), Y ) }.
% 1.26/1.63 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.26/1.63 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.26/1.63 skol11( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 1.26/1.63 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.26/1.63 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 1.26/1.63 , skol11( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.26/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.26/1.63 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 1.26/1.63 }.
% 1.26/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.26/1.63 , alpha47( X, Y, Z, T ) }.
% 1.26/1.63 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha47( X, Y, Z, T ),
% 1.26/1.63 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 1.26/1.63 { ! alpha47( X, Y, Z, T ), alpha12( X, Z, T ) }.
% 1.26/1.63 { ! alpha47( X, Y, Z, T ), alpha33( X, Y, T ) }.
% 1.26/1.63 { ! alpha12( X, Z, T ), ! alpha33( X, Y, T ), alpha47( X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha33( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ), alpha48( X, Y, Z ) }.
% 1.26/1.63 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha33( X
% 1.26/1.63 , Y, Z ) }.
% 1.26/1.63 { ! alpha48( X, Y, Z ), alpha33( X, Y, Z ) }.
% 1.26/1.63 { ! alpha48( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.63 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 1.26/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha48( X
% 1.26/1.63 , Y, Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 1.26/1.63 ), c_Polynomial_Odegree( X, Z ) ), alpha48( X, Y, Z ) }.
% 1.26/1.63 { ! alpha12( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha12( X,
% 1.26/1.63 Y, Z ) }.
% 1.26/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha12( X
% 1.26/1.63 , Y, Z ) }.
% 1.26/1.63 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.26/1.63 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 1.26/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 1.26/1.63 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.26/1.63 ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( tc_Nat_Onat, Y, Z ), X ) }.
% 1.26/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.26/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 1.26/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.26/1.63 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.26/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.26/1.63 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.26/1.63 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 1.26/1.63 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 1.26/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 1.26/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.26/1.63 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 1.26/1.63 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 1.26/1.63 tc_Nat_Onat ) ) }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.26/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 1.26/1.63 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.26/1.63 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Y, X ), Y ) = X }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Y, X ), X ) = Y }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 1.26/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.26/1.63 c_Polynomial_Odegree( X, Y ) }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( tc_Nat_Onat, Z, Y ), X ) }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.26/1.63 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 1.26/1.63 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 1.26/1.63 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 1.26/1.63 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 1.26/1.63 hAPP( Z, Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.26/1.63 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.26/1.63 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.26/1.63 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.26/1.63 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 1.26/1.63 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.26/1.63 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.26/1.63 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 1.26/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) =
% 1.26/1.63 c_Polynomial_Odegree( X, Z ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.26/1.63 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.26/1.63 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.26/1.63 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.26/1.63 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.26/1.63 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.26/1.63 c_Polynomial_Odegree( X, Y ) ), ! c_Rings_Odvd__class_Odvd(
% 1.26/1.63 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 1.26/1.63 tc_Polynomial_Opoly( X ), Y, Z ), Z = Y }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.26/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Z, Y ), X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, X, Z ), Y ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Z, X ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Nat_Onat, X, Y ), Y ) = X }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 1.26/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X )
% 1.26/1.63 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 1.26/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.26/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y )
% 1.26/1.63 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 1.26/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 1.26/1.63 , c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Z, Y ) ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.26/1.63 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.26/1.63 ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 1.26/1.63 ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Z, X ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.26/1.63 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 1.26/1.63 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 1.26/1.63 { ! class_Groups_Ocomm__monoid__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.26/1.63 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 1.26/1.63 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.26/1.63 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.26/1.63 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.26/1.63 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.26/1.63 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.26/1.63 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.26/1.63 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.26/1.63 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 1.26/1.63 .
% 1.26/1.63 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.63 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.26/1.63 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) )
% 1.26/1.63 , c_Polynomial_Odegree( X, Y ) ) }.
% 1.26/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 1.26/1.63 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 1.26/1.63 , Y ) ) }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 1.26/1.63 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 1.26/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.26/1.63 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 1.26/1.63 X, Y ) ) }.
% 1.26/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.26/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.26/1.63 X, Z, Y ) }.
% 1.26/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.26/1.63 X, Y ) }.
% 1.26/1.63 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.26/1.63 Z ) ), Y ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.26/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.26/1.63 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.26/1.63 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 1.26/1.63 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.26/1.63 Z ) ), U ), T ) = Y }.
% 1.26/1.63 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.26/1.63 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), Z ), U ), Y ) }.
% 1.26/1.63 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.26/1.63 W ) ), U ), Y ) }.
% 1.26/1.63 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.26/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.26/1.63 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), Z ), U ), Y ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( X ) ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.26/1.63 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.26/1.63 , Z, Y ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.26/1.63 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.26/1.63 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.26/1.63 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.26/1.63 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.63 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.63 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 1.26/1.63 c_Polynomial_Odegree( X, Y ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.63 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 1.26/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 1.26/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.26/1.63 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.26/1.63 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.26/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.26/1.63 X, W, Z ) ), U ), T ), Y ) }.
% 1.26/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.26/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), Z ), U ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.26/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( X, Z, W ) ), U ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.26/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.26/1.63 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 1.26/1.63 tc_Nat_Onat, Y, c_Polynomial_Odegree( X, Z ) ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 1.26/1.63 , c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Z, Y ) ), c_Nat_OSuc(
% 1.26/1.63 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.26/1.63 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.26/1.63 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.26/1.63 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 1.26/1.63 .
% 1.26/1.63 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.26/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.26/1.63 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.26/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.26/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.26/1.63 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.26/1.63 }.
% 1.26/1.63 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.26/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.26/1.63 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.26/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.26/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.26/1.63 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.26/1.63 }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.26/1.63 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.26/1.63 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.26/1.63 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 1.26/1.63 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.26/1.63 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.26/1.63 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ),
% 1.26/1.63 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.26/1.63 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.26/1.63 ( X ), Z, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X )
% 1.26/1.63 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree
% 1.26/1.63 ( X, Z ), c_Polynomial_Odegree( X, Y ) ) }.
% 1.26/1.63 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 1.26/1.63 c_Polynomial_Odegree( X, Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 1.26/1.63 ) ) = X }.
% 1.26/1.63 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.26/1.63 , ! alpha13( X, Y, Z ) }.
% 1.26/1.63 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.26/1.63 , ! alpha34( X, Y, Z ) }.
% 1.26/1.63 { alpha13( X, Y, Z ), alpha34( X, Y, Z ), hBOOL( hAPP( Z,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.26/1.63 { ! alpha34( X, Y, Z ), ! hBOOL( hAPP( Z, skol12( T, U, Z ) ) ) }.
% 1.26/1.63 { ! alpha34( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.26/1.63 skol12( X, Y, Z ) ) }.
% 1.26/1.63 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 1.26/1.63 ) ), alpha34( X, Y, Z ) }.
% 1.26/1.63 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.26/1.63 }.
% 1.26/1.63 { ! alpha13( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ) ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha13( X, Y, Z ) }.
% 1.26/1.63 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.26/1.63 , alpha14( X, Y, Z ) }.
% 1.26/1.63 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.26/1.63 , alpha35( X, Y, Z ) }.
% 1.26/1.63 { ! alpha14( X, Y, Z ), ! alpha35( X, Y, Z ), hBOOL( hAPP( Z,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.26/1.63 { ! alpha35( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.26/1.63 T ), hBOOL( hAPP( Z, T ) ) }.
% 1.26/1.63 { ! hBOOL( hAPP( Z, skol13( T, U, Z ) ) ), alpha35( X, Y, Z ) }.
% 1.26/1.63 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol13( X, Y, Z ) ),
% 1.26/1.63 alpha35( X, Y, Z ) }.
% 1.26/1.63 { ! alpha14( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.26/1.63 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha14( X, Y, Z ) }
% 1.26/1.63 .
% 1.26/1.63 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha14
% 1.26/1.63 ( X, Y, Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.26/1.63 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.26/1.63 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Orderings_Oord__class_Oless__eq
% 1.26/1.63 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Polynomial_Odegree( X, Z ) ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 1.26/1.63 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.26/1.63 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.26/1.63 }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 1.26/1.63 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 1.26/1.63 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.26/1.63 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Opcompose( X, Z, Y )
% 1.26/1.63 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.26/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y
% 1.26/1.63 , X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ), c_Polynomial_Odegree(
% 1.26/1.63 tc_Complex_Ocomplex, X ) ), X = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.26/1.63 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.26/1.63 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.26/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.26/1.63 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.26/1.63 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.26/1.63 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.26/1.63 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.26/1.63 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.26/1.63 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.26/1.63 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 1.26/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 1.26/1.63 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.26/1.63 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.26/1.63 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.26/1.63 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.26/1.63 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.26/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.26/1.63 ( tc_Nat_Onat ) ) ), X ) ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ),
% 1.26/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ),
% 1.26/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 1.26/1.63 c_Polynomial_Odegree( X, Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 1.26/1.63 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 1.26/1.63 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.26/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 1.26/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 1.26/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.26/1.63 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.26/1.63 ( tc_Nat_Onat ) ) ) ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.26/1.63 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), ! hAPP(
% 1.26/1.63 c_Polynomial_Ocoeff( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 1.26/1.63 , Y ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 1.26/1.63 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.26/1.63 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.26/1.63 { ! alpha15( X, Y ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.26/1.63 tc_Complex_Ocomplex ), Y, hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.26/1.63 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), X ), c_Polynomial_Odegree(
% 1.26/1.63 tc_Complex_Ocomplex, Y ) ) ), alpha36( X, Y ) }.
% 1.26/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y
% 1.26/1.63 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 1.26/1.63 tc_Complex_Ocomplex ) ), X ), c_Polynomial_Odegree( tc_Complex_Ocomplex,
% 1.26/1.63 Y ) ) ), alpha15( X, Y ) }.
% 1.26/1.63 { ! alpha36( X, Y ), alpha15( X, Y ) }.
% 1.26/1.63 { ! alpha36( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.26/1.63 tc_Complex_Ocomplex ) ) }.
% 1.26/1.63 { ! alpha36( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.26/1.63 tc_Complex_Ocomplex ) ) }.
% 1.26/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.26/1.63 tc_Complex_Ocomplex ) ), ! X = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), alpha36( X, Y ) }.
% 1.26/1.63 { ! alpha15( X, Y ), ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ),
% 1.26/1.63 Z ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 1.26/1.63 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), Z ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), skol14( Z, Y ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), alpha15( X, Y ) }.
% 1.26/1.63 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol14( X, Y ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), alpha15( X, Y ) }.
% 1.26/1.63 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.26/1.63 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.26/1.63 c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.63 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.26/1.63 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.26/1.63 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.26/1.63 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 1.26/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.26/1.63 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.26/1.63 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 1.26/1.63 }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.26/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), ! T =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Y ), T ), hAPP(
% 1.26/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Z ), X ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Y ), T ), hAPP(
% 1.26/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Z ), X ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), T =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 1.26/1.63 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.26/1.63 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.26/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.26/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.26/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.26/1.63 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.26/1.63 T ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Polynomial_Odegree( X, c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), Y ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.26/1.63 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.26/1.63 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.26/1.63 .
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.26/1.63 ( tc_Int_Oint ) ) ) }.
% 1.26/1.63 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), skol15( Z, Y ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 1.26/1.63 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = T, T =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.26/1.63 tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y, hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 1.26/1.63 ), X ), T ) ) }.
% 1.26/1.63 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol15( X, Y ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 1.26/1.63 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = Z, Z =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.26/1.63 tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y, hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 1.26/1.63 ), X ), Z ) ) }.
% 1.26/1.63 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.26/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( X, X,
% 1.26/1.63 c_Polynomial_Opoly( X, Y ) ), c_Polynomial_Odegree( X, Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.26/1.63 c_Polynomial_Odegree( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.26/1.63 , c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( X, X,
% 1.26/1.63 c_Polynomial_Opoly( X, Y ) ) }.
% 1.26/1.63 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 1.26/1.63 X, T ) = hAPP( X, U ) }.
% 1.26/1.63 { ! hAPP( X, skol16( X ) ) = hAPP( X, skol18( X ) ),
% 1.26/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 1.26/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.26/1.63 , T = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! V0 =
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 1.26/1.63 c_Polynomial_OpCons( X, W, Y ) ), c_Polynomial_Odegree( X, T ) ), hAPP(
% 1.26/1.63 c_Polynomial_Ocoeff( X, T ), c_Polynomial_Odegree( X, T ) ) ),
% 1.26/1.63 c_Polynomial_Opdivmod__rel( X, c_Polynomial_OpCons( X, W, U ), T,
% 1.26/1.63 c_Polynomial_OpCons( X, V0, Z ), c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, W, Y ),
% 1.26/1.63 c_Polynomial_Osmult( X, V0, T ) ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.26/1.63 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Int_Oint, X, Y ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.26/1.63 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__field( X ),
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.26/1.63 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.26/1.63 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.26/1.63 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.26/1.63 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 1.26/1.63 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.26/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.26/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 1.26/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.26/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 1.26/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.26/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.26/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.26/1.63 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 1.26/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.26/1.63 c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 1.26/1.63 ( X ) }.
% 1.26/1.63 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.26/1.63 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.26/1.63 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.63 , Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 1.26/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.26/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X
% 1.26/1.63 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.26/1.63 { ! class_Rings_Odivision__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.26/1.63 ), Y ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__field( X ),
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.26/1.63 ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.26/1.63 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 1.26/1.63 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.26/1.63 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__field( X ),
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 1.26/1.63 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 1.26/1.63 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__field( X ),
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.26/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 }.
% 1.26/1.63 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 1.26/1.63 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 1.26/1.63 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.63 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 1.26/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.26/1.63 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 1.26/1.63 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.26/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Nat_Onat, Z, T ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 1.26/1.63 ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.26/1.63 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Int_Oint, X, Y ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.26/1.63 ( X, Z, Y ) ), alpha37( X, Y, Z, T ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.26/1.63 ( X, Z, Y ) ), alpha49( X, Y, Z, T ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha37( X, Y, Z
% 1.26/1.63 , T ), ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.26/1.63 { ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ), alpha53( X, Y, Z, T ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.26/1.63 , alpha49( X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha53( X, Y, Z, T ), alpha49( X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha53( X, Y, Z, T ), alpha57( X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha53( X, Y, Z, T ), alpha16( X, Y, T ) }.
% 1.26/1.63 { ! alpha57( X, Y, Z, T ), ! alpha16( X, Y, T ), alpha53( X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha57( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.63 alpha57( X, Y, Z, T ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha57( X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha37( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 1.26/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.63 alpha37( X, Y, Z, T ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha37( X, Y, Z, T )
% 1.26/1.63 }.
% 1.26/1.63 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.63 , alpha16( X, Y, Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.26/1.63 ) ), alpha16( X, Y, Z ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.63 , T, Z ), Y ), alpha38( X, Y, Z, T ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.63 , T, Z ), Y ), alpha50( X, Y, Z, T ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha38( X, Y, Z
% 1.26/1.63 , T ), ! alpha50( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 1.26/1.63 { ! alpha50( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Z ), alpha54( X, Y, Z, T ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.26/1.63 , alpha50( X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha54( X, Y, Z, T ), alpha50( X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha54( X, Y, Z, T ), alpha58( X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha54( X, Y, Z, T ), alpha17( X, Y, Z ) }.
% 1.26/1.63 { ! alpha58( X, Y, Z, T ), ! alpha17( X, Y, Z ), alpha54( X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha58( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.63 alpha58( X, Y, Z, T ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha58( X, Y, Z, T )
% 1.26/1.63 }.
% 1.26/1.63 { ! alpha38( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 1.26/1.63 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.26/1.63 alpha38( X, Y, Z, T ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha38( X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.63 , alpha17( X, Y, Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , Y ), alpha17( X, Y, Z ) }.
% 1.26/1.63 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 1.26/1.63 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.63 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.26/1.63 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.26/1.63 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 1.26/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.26/1.63 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.26/1.63 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha18( X, Y, Z ), alpha39
% 1.26/1.63 ( X, Y, Z ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha18( X, Y, Z
% 1.26/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.26/1.63 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha39( X, Y, Z
% 1.26/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.26/1.63 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.26/1.63 { ! alpha39( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! alpha39( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.26/1.63 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), alpha39( X, Y, Z ) }.
% 1.26/1.63 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.26/1.63 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ), alpha18( X, Y, Z ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.63 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha19( X, Y, Z ), alpha40
% 1.26/1.63 ( X, Y, Z ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha19( X, Y, Z
% 1.26/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.26/1.63 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha40( X, Y, Z
% 1.26/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.26/1.63 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! alpha40( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! alpha40( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.26/1.63 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( X ), Y ), alpha40( X, Y, Z ) }.
% 1.26/1.63 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.26/1.63 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), alpha19( X, Y, Z ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.26/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.26/1.63 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.26/1.63 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.26/1.63 , Y, Z ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.26/1.63 , Y, Z ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 1.26/1.63 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha20( X, Y, Z ), alpha41( X,
% 1.26/1.63 Y, Z ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha20( X, Y, Z
% 1.26/1.63 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.63 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha41( X, Y, Z
% 1.26/1.63 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.63 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! alpha41( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! alpha41( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.63 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 ), alpha41( X, Y, Z ) }.
% 1.26/1.63 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.26/1.63 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.26/1.63 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 ), alpha20( X, Y, Z ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha21( X, Y, Z ), alpha42
% 1.26/1.63 ( X, Y, Z ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha21( X, Y, Z
% 1.26/1.63 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha42( X, Y, Z
% 1.26/1.63 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.26/1.63 { ! alpha42( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! alpha42( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.63 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 ), alpha42( X, Y, Z ) }.
% 1.26/1.63 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.26/1.63 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.26/1.63 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 ), alpha21( X, Y, Z ) }.
% 1.26/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 1.26/1.63 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 1.26/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.26/1.63 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.26/1.63 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.26/1.63 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha43( X, Y, Z, T ) }.
% 1.26/1.63 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha22( X, Y, Z ) }.
% 1.26/1.63 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha43( X, Y, Z, T ), !
% 1.26/1.63 alpha22( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 1.26/1.63 { ! alpha43( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 1.26/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.26/1.63 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha43( X, Y, Z, T ) }.
% 1.26/1.63 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha43(
% 1.26/1.63 X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha22( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { Z = c_Groups_Ozero__class_Ozero( X ), alpha22( X, Y, Z ) }.
% 1.26/1.63 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha22( X, Y, Z ) }.
% 1.26/1.63 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha44( X, Y, Z, T ) }.
% 1.26/1.63 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha23( X, Y, T ) }.
% 1.26/1.63 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha44( X, Y, Z, T ), !
% 1.26/1.63 alpha23( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.26/1.63 { ! alpha44( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 1.26/1.63 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.26/1.63 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha44( X, Y, Z, T ) }.
% 1.26/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha44(
% 1.26/1.63 X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha23( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { Y = c_Groups_Ozero__class_Ozero( X ), alpha23( X, Y, Z ) }.
% 1.26/1.63 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha23( X, Y, Z ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.26/1.63 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 1.26/1.63 X ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.26/1.63 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.63 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.26/1.63 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 1.26/1.63 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.26/1.63 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.26/1.63 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 1.26/1.63 X ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.26/1.63 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.26/1.63 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.26/1.63 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.26/1.63 Y ), Z ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.63 Z, Y ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.63 Z, Y ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.26/1.63 Y ), Z ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.26/1.63 Y ), Z ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.63 Z, Y ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.26/1.63 Z ), Y ), alpha45( X, Y, Z, T ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.26/1.63 Z ), Y ), alpha51( X, Y, Z, T ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha45( X, Y, Z
% 1.26/1.63 , T ), ! alpha51( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 1.26/1.63 { ! alpha51( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Z ), alpha55( X, Y, Z, T ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.26/1.63 , alpha51( X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha55( X, Y, Z, T ), alpha51( X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha55( X, Y, Z, T ), alpha59( X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha55( X, Y, Z, T ), alpha24( X, Y, Z ) }.
% 1.26/1.63 { ! alpha59( X, Y, Z, T ), ! alpha24( X, Y, Z ), alpha55( X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha59( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.63 alpha59( X, Y, Z, T ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha59( X, Y, Z, T )
% 1.26/1.63 }.
% 1.26/1.63 { ! alpha45( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.26/1.63 alpha45( X, Y, Z, T ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha45( X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.63 , alpha24( X, Y, Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.26/1.63 , alpha24( X, Y, Z ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.63 Z, Y ) ), alpha46( X, Y, Z, T ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.63 Z, Y ) ), alpha52( X, Y, Z, T ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha46( X, Y, Z
% 1.26/1.63 , T ), ! alpha52( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.26/1.63 { ! alpha52( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ), alpha56( X, Y, Z, T ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.26/1.63 , alpha52( X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha56( X, Y, Z, T ), alpha52( X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha56( X, Y, Z, T ), alpha60( X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha56( X, Y, Z, T ), alpha25( X, Y, T ) }.
% 1.26/1.63 { ! alpha60( X, Y, Z, T ), ! alpha25( X, Y, T ), alpha56( X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha60( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.63 alpha60( X, Y, Z, T ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha60( X, Y, Z, T ) }.
% 1.26/1.63 { ! alpha46( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.63 alpha46( X, Y, Z, T ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha46( X, Y, Z, T )
% 1.26/1.63 }.
% 1.26/1.63 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.63 , alpha25( X, Y, Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.63 , alpha25( X, Y, Z ) }.
% 1.26/1.63 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 1.26/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 1.26/1.63 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 1.26/1.63 .
% 1.26/1.63 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 1.26/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 1.26/1.63 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 1.26/1.63 .
% 1.26/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.26/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.26/1.63 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 1.26/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.63 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.26/1.63 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.26/1.63 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.26/1.63 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.26/1.63 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.63 , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.63 , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.63 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.63 , T, Y ), Z ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.26/1.63 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.26/1.63 ( X, Z, Y ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.26/1.63 ( X, Z, Y ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.63 , T, Y ), Z ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.63 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.63 , T, Y ), Z ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.26/1.63 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.26/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.26/1.63 ( X, Z, Y ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 1.26/1.63 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 1.26/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 1.26/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T, Z ), Y ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.26/1.63 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 1.26/1.63 tc_Polynomial_Opoly( X ), Z, Y ) ), c_Polynomial_Osmult( X,
% 1.26/1.63 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 1.26/1.63 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 1.26/1.63 tc_Polynomial_Opoly( X ), Z, Y ) ) ), c_Polynomial_Odegree( X, Y ) ),
% 1.26/1.63 hAPP( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y )
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.26/1.63 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 1.26/1.63 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 1.26/1.63 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.26/1.63 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.26/1.63 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.26/1.63 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.26/1.63 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 1.26/1.63 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 1.26/1.63 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.26/1.63 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.26/1.63 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 1.26/1.63 ( tc_fun( Y, X ) ) }.
% 1.26/1.63 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.26/1.63 ) ) }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.26/1.63 .
% 1.26/1.63 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.26/1.63 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 1.26/1.63 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 1.26/1.63 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.26/1.63 tc_Int_Oint ) }.
% 1.26/1.63 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.26/1.63 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.26/1.63 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.26/1.63 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.26/1.63 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.26/1.63 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.26/1.63 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.26/1.63 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.26/1.63 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.26/1.63 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.26/1.63 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.26/1.63 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.26/1.63 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.26/1.63 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.26/1.63 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.26/1.63 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.26/1.63 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.26/1.63 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.26/1.63 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.26/1.63 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.26/1.63 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.26/1.63 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.26/1.63 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.26/1.63 { class_Groups_Ominus( tc_Int_Oint ) }.
% 1.26/1.63 { class_Power_Opower( tc_Int_Oint ) }.
% 1.26/1.63 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.26/1.63 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.26/1.63 { class_Rings_Odvd( tc_Int_Oint ) }.
% 1.26/1.63 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.26/1.63 tc_Nat_Onat ) }.
% 1.26/1.63 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 1.26/1.63 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 1.26/1.63 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.26/1.63 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.26/1.63 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.26/1.63 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 1.26/1.63 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 1.26/1.63 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.26/1.63 tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { ! class_Rings_Oidom( X ),
% 1.26/1.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.63 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.26/1.63 ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.63 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.26/1.63 X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.63 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.63 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.26/1.63 }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.63 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.63 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.63 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.63 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.26/1.63 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.63 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.63 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.63 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.63 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.63 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.26/1.63 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.26/1.63 ( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.26/1.63 ( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 1.26/1.63 ( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.26/1.63 }.
% 1.26/1.63 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.26/1.63 ) ) }.
% 1.26/1.63 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.26/1.63 .
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 1.26/1.63 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 1.26/1.63 { ! c_Polynomial_Osmult( tc_Complex_Ocomplex, v_a, v_q ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 1.26/1.63 ), v_q ), c_Polynomial_OpCons( tc_Complex_Ocomplex, v_a,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 1.26/1.63 ) ) }.
% 1.26/1.63
% 1.26/1.63 *** allocated 15000 integers for clauses
% 1.26/1.63 *** allocated 22500 integers for clauses
% 1.26/1.63 *** allocated 33750 integers for clauses
% 1.26/1.63 *** allocated 50625 integers for clauses
% 1.26/1.63 *** allocated 75937 integers for clauses
% 1.26/1.63 percentage equality = 0.252594, percentage horn = 0.890735
% 1.26/1.63 This is a problem with some equality
% 1.26/1.63
% 1.26/1.63
% 1.26/1.63
% 1.26/1.63 Options Used:
% 1.26/1.63
% 1.26/1.63 useres = 1
% 1.26/1.63 useparamod = 1
% 1.26/1.63 useeqrefl = 1
% 1.26/1.63 useeqfact = 1
% 1.26/1.63 usefactor = 1
% 1.26/1.63 usesimpsplitting = 0
% 1.26/1.63 usesimpdemod = 5
% 1.26/1.63 usesimpres = 3
% 1.26/1.63
% 1.26/1.63 resimpinuse = 1000
% 1.26/1.63 resimpclauses = 20000
% 1.26/1.63 substype = eqrewr
% 1.26/1.63 backwardsubs = 1
% 1.26/1.63 selectoldest = 5
% 1.26/1.63
% 1.26/1.63 litorderings [0] = split
% 1.26/1.63 litorderings [1] = extend the termordering, first sorting on arguments
% 1.26/1.63
% 1.26/1.63 termordering = kbo
% 1.26/1.63
% 1.26/1.63 litapriori = 0
% 1.26/1.63 termapriori = 1
% 1.26/1.63 litaposteriori = 0
% 1.26/1.63 termaposteriori = 0
% 1.26/1.63 demodaposteriori = 0
% 1.26/1.63 ordereqreflfact = 0
% 1.26/1.63
% 1.26/1.63 litselect = negord
% 1.26/1.63
% 1.26/1.63 maxweight = 15
% 1.26/1.63 maxdepth = 30000
% 1.26/1.63 maxlength = 115
% 1.26/1.63 maxnrvars = 195
% 1.26/1.63 excuselevel = 1
% 1.26/1.63 increasemaxweight = 1
% 1.26/1.63
% 1.26/1.63 maxselected = 10000000
% 1.26/1.63 maxnrclauses = 10000000
% 1.26/1.63
% 1.26/1.63 showgenerated = 0
% 1.26/1.63 showkept = 0
% 1.26/1.63 showselected = 0
% 1.26/1.63 showdeleted = 0
% 1.26/1.63 showresimp = 1
% 1.26/1.63 showstatus = 2000
% 1.26/1.63
% 1.26/1.63 prologoutput = 0
% 1.26/1.63 nrgoals = 5000000
% 1.26/1.63 totalproof = 1
% 1.26/1.63
% 1.26/1.63 Symbols occurring in the translation:
% 1.26/1.63
% 1.26/1.63 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.26/1.63 . [1, 2] (w:1, o:185, a:1, s:1, b:0),
% 1.26/1.63 ! [4, 1] (w:0, o:101, a:1, s:1, b:0),
% 1.26/1.63 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.26/1.63 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.26/1.63 hAPP [38, 2] (w:1, o:209, a:1, s:1, b:0),
% 1.26/1.63 tc_Complex_Ocomplex [39, 0] (w:1, o:11, a:1, s:1, b:0),
% 1.26/1.63 tc_Polynomial_Opoly [40, 1] (w:1, o:109, a:1, s:1, b:0),
% 1.26/1.63 v_p [41, 0] (w:1, o:12, a:1, s:1, b:0),
% 1.26/1.63 v_q [42, 0] (w:1, o:13, a:1, s:1, b:0),
% 1.26/1.63 c_Rings_Odvd__class_Odvd [43, 3] (w:1, o:237, a:1, s:1, b:0),
% 1.26/1.63 class_Rings_Ocomm__semiring__0 [48, 1] (w:1, o:112, a:1, s:1, b:0),
% 1.26/1.63 c_Polynomial_Osmult [49, 3] (w:1, o:240, a:1, s:1, b:0),
% 1.26/1.63 c_Polynomial_OpCons [50, 3] (w:1, o:242, a:1, s:1, b:0),
% 1.26/1.63 c_Groups_Ozero__class_Ozero [51, 1] (w:1, o:113, a:1, s:1, b:0),
% 1.26/1.63 c_Groups_Otimes__class_Otimes [53, 1] (w:1, o:114, a:1, s:1, b:0),
% 1.26/1.63 class_Rings_Oidom [56, 1] (w:1, o:115, a:1, s:1, b:0),
% 1.26/1.63 class_Groups_Ozero [57, 1] (w:1, o:120, a:1, s:1, b:0),
% 1.26/1.63 class_Rings_Ocomm__semiring__1 [59, 1] (w:1, o:121, a:1, s:1, b:0),
% 1.26/1.63 class_Fields_Ofield [60, 1] (w:1, o:116, a:1, s:1, b:0),
% 1.26/1.63 class_Rings_Odvd [65, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.26/1.63 class_Rings_Omult__zero [67, 1] (w:1, o:133, a:1, s:1, b:0),
% 1.26/1.63 class_Rings_Oring__no__zero__divisors [68, 1] (w:1, o:134, a:1, s:1
% 1.26/1.63 , b:0),
% 1.26/1.63 class_Rings_Ono__zero__divisors [69, 1] (w:1, o:135, a:1, s:1, b:0),
% 1.26/1.63
% 1.26/1.63 class_RealVector_Oreal__normed__algebra [70, 1] (w:1, o:136, a:1, s:1
% 1.26/1.63 , b:0),
% 1.26/1.63 c_Polynomial_Opoly__rec [75, 5] (w:1, o:313, a:1, s:1, b:0),
% 1.26/1.63 c_fequal [76, 2] (w:1, o:210, a:1, s:1, b:0),
% 1.26/1.63 c_If [77, 4] (w:1, o:288, a:1, s:1, b:0),
% 1.26/1.63 c_Groups_Oplus__class_Oplus [78, 3] (w:1, o:245, a:1, s:1, b:0),
% 1.26/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [80, 3] (w:1
% 1.26/1.63 , o:243, a:1, s:1, b:0),
% 1.26/1.63 class_Groups_Ocomm__monoid__add [81, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.26/1.63
% 1.26/1.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [82
% 1.26/1.63 , 1] (w:1, o:152, a:1, s:1, b:0),
% 1.26/1.63 class_Rings_Osemiring [94, 1] (w:1, o:141, a:1, s:1, b:0),
% 1.26/1.63 class_Rings_Ocomm__semiring [95, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.26/1.63 class_Rings_Osemiring__0 [104, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.26/1.63 hBOOL [105, 1] (w:1, o:153, a:1, s:1, b:0),
% 1.26/1.63 c_Polynomial_Opcompose [106, 3] (w:1, o:246, a:1, s:1, b:0),
% 1.26/1.63 class_Rings_Olinordered__ring__strict [107, 1] (w:1, o:124, a:1, s:1
% 1.26/1.63 , b:0),
% 1.26/1.63 class_Groups_Olinordered__ab__group__add [108, 1] (w:1, o:154, a:1
% 1.26/1.63 , s:1, b:0),
% 1.26/1.63 class_Groups_Omonoid__add [109, 1] (w:1, o:155, a:1, s:1, b:0),
% 1.26/1.63 c_Polynomial_Opoly [110, 2] (w:1, o:211, a:1, s:1, b:0),
% 1.26/1.63 class_Int_Oring__char__0 [111, 1] (w:1, o:156, a:1, s:1, b:0),
% 1.26/1.63 class_Groups_Oab__semigroup__mult [112, 1] (w:1, o:157, a:1, s:1, b:0
% 1.26/1.63 ),
% 1.26/1.63 class_Groups_Ocancel__semigroup__add [113, 1] (w:1, o:158, a:1, s:1
% 1.26/1.63 , b:0),
% 1.26/1.63 class_Groups_Ocancel__ab__semigroup__add [114, 1] (w:1, o:159, a:1
% 1.26/1.63 , s:1, b:0),
% 1.26/1.63 class_Groups_Oab__semigroup__add [115, 1] (w:1, o:160, a:1, s:1, b:0)
% 1.26/1.63 ,
% 1.26/1.63 c_Polynomial_Osynthetic__div [116, 3] (w:1, o:247, a:1, s:1, b:0),
% 1.26/1.63 c_Polynomial_Oorder [117, 3] (w:1, o:241, a:1, s:1, b:0),
% 1.26/1.63 tc_Nat_Onat [118, 0] (w:1, o:67, a:1, s:1, b:0),
% 1.26/1.63 c_Groups_Oone__class_Oone [119, 1] (w:1, o:161, a:1, s:1, b:0),
% 1.26/1.63 c_Polynomial_Opdivmod__rel [122, 5] (w:1, o:314, a:1, s:1, b:0),
% 1.26/1.63 class_Lattices_Oab__semigroup__idem__mult [123, 1] (w:1, o:162, a:1
% 1.26/1.63 , s:1, b:0),
% 1.26/1.63 class_Groups_Oone [124, 1] (w:1, o:163, a:1, s:1, b:0),
% 1.26/1.63 class_Rings_Ozero__neq__one [129, 1] (w:1, o:143, a:1, s:1, b:0),
% 1.26/1.63 class_Groups_Ocomm__monoid__mult [130, 1] (w:1, o:164, a:1, s:1, b:0)
% 1.26/1.63 ,
% 1.26/1.63 class_Groups_Omonoid__mult [131, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.26/1.63 class_Rings_Ocomm__ring__1 [133, 1] (w:1, o:110, a:1, s:1, b:0),
% 1.26/1.63 c_Groups_Ouminus__class_Ouminus [134, 2] (w:1, o:213, a:1, s:1, b:0)
% 1.26/1.63 ,
% 1.26/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [135, 2] (w:1, o:
% 1.26/1.63 212, a:1, s:1, b:0),
% 1.26/1.63 c_Polynomial_Omonom [136, 3] (w:1, o:248, a:1, s:1, b:0),
% 1.26/1.63 class_Rings_Olinordered__semiring__1 [139, 1] (w:1, o:126, a:1, s:1
% 1.26/1.63 , b:0),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq [140, 3] (w:1, o:238, a:1, s:1, b:0
% 1.26/1.63 ),
% 1.26/1.63 class_Groups_Oordered__ab__group__add [144, 1] (w:1, o:166, a:1, s:1
% 1.26/1.63 , b:0),
% 1.26/1.63 class_Lattices_Oboolean__algebra [145, 1] (w:1, o:167, a:1, s:1, b:0)
% 1.26/1.63 ,
% 1.26/1.63 class_Groups_Ouminus [147, 1] (w:1, o:168, a:1, s:1, b:0),
% 1.26/1.63 tc_fun [148, 2] (w:1, o:223, a:1, s:1, b:0),
% 1.26/1.63 class_Groups_Oab__group__add [149, 1] (w:1, o:169, a:1, s:1, b:0),
% 1.26/1.63 class_Rings_Ocomm__ring [150, 1] (w:1, o:111, a:1, s:1, b:0),
% 1.26/1.63 class_Groups_Ogroup__add [151, 1] (w:1, o:170, a:1, s:1, b:0),
% 1.26/1.63 class_Rings_Oring [157, 1] (w:1, o:138, a:1, s:1, b:0),
% 1.26/1.63 class_Groups_Oordered__ab__semigroup__add__imp__le [158, 1] (w:1, o:
% 1.26/1.63 171, a:1, s:1, b:0),
% 1.26/1.63 class_Groups_Oordered__ab__semigroup__add [159, 1] (w:1, o:172, a:1
% 1.26/1.63 , s:1, b:0),
% 1.26/1.63 class_Rings_Oring__1__no__zero__divisors [160, 1] (w:1, o:139, a:1
% 1.26/1.63 , s:1, b:0),
% 1.26/1.63 class_Rings_Olinordered__ring [161, 1] (w:1, o:125, a:1, s:1, b:0),
% 1.26/1.63 class_Rings_Oordered__cancel__semiring [162, 1] (w:1, o:144, a:1, s:1
% 1.26/1.63 , b:0),
% 1.26/1.63 class_Rings_Oordered__ring [163, 1] (w:1, o:145, a:1, s:1, b:0),
% 1.26/1.63 class_Rings_Oordered__semiring [164, 1] (w:1, o:146, a:1, s:1, b:0),
% 1.26/1.63
% 1.26/1.63 class_Rings_Oordered__comm__semiring [165, 1] (w:1, o:147, a:1, s:1
% 1.48/1.90 , b:0),
% 1.48/1.90 class_Groups_Oordered__comm__monoid__add [166, 1] (w:1, o:173, a:1
% 1.48/1.90 , s:1, b:0),
% 1.48/1.90 class_Rings_Olinordered__semidom [167, 1] (w:1, o:127, a:1, s:1, b:0)
% 1.48/1.90 ,
% 1.48/1.90 class_Rings_Olinordered__idom [168, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.48/1.90 class_Orderings_Opreorder [169, 1] (w:1, o:176, a:1, s:1, b:0),
% 1.48/1.90 c_Power_Opower__class_Opower [170, 1] (w:1, o:177, a:1, s:1, b:0),
% 1.48/1.90 class_Rings_Olinordered__semiring__1__strict [171, 1] (w:1, o:129, a:
% 1.48/1.90 1, s:1, b:0),
% 1.48/1.90 c_Orderings_Oord__class_Oless [172, 3] (w:1, o:239, a:1, s:1, b:0),
% 1.48/1.90 c_Polynomial_Ocoeff [173, 2] (w:1, o:224, a:1, s:1, b:0),
% 1.48/1.90 class_Orderings_Oorder [174, 1] (w:1, o:174, a:1, s:1, b:0),
% 1.48/1.90 class_Orderings_Olinorder [175, 1] (w:1, o:178, a:1, s:1, b:0),
% 1.48/1.90 tc_Int_Oint [176, 0] (w:1, o:85, a:1, s:1, b:0),
% 1.48/1.90 class_Orderings_Oord [177, 1] (w:1, o:175, a:1, s:1, b:0),
% 1.48/1.90 class_Groups_Oordered__cancel__ab__semigroup__add [179, 1] (w:1, o:
% 1.48/1.90 179, a:1, s:1, b:0),
% 1.48/1.90 class_Rings_Olinordered__comm__semiring__strict [180, 1] (w:1, o:130
% 1.48/1.90 , a:1, s:1, b:0),
% 1.48/1.90 class_Rings_Olinordered__semiring__strict [181, 1] (w:1, o:131, a:1
% 1.48/1.90 , s:1, b:0),
% 1.48/1.90 class_Rings_Olinordered__semiring [182, 1] (w:1, o:132, a:1, s:1, b:0
% 1.48/1.90 ),
% 1.48/1.90 class_Power_Opower [191, 1] (w:1, o:180, a:1, s:1, b:0),
% 1.48/1.90 class_Rings_Oring__1 [192, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.48/1.90 c_Nat_OSuc [193, 1] (w:1, o:181, a:1, s:1, b:0),
% 1.48/1.90 c_Power_Opower_Opower [194, 3] (w:1, o:249, a:1, s:1, b:0),
% 1.48/1.90 c_Polynomial_Opos__poly [205, 2] (w:1, o:225, a:1, s:1, b:0),
% 1.48/1.90 c_Polynomial_Odegree [207, 2] (w:1, o:226, a:1, s:1, b:0),
% 1.48/1.90 c_Groups_Ominus__class_Ominus [208, 3] (w:1, o:250, a:1, s:1, b:0),
% 1.48/1.90 class_Groups_Ominus [210, 1] (w:1, o:182, a:1, s:1, b:0),
% 1.48/1.90 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [217, 3] (w:1
% 1.48/1.90 , o:244, a:1, s:1, b:0),
% 1.48/1.90 c_Rings_Oinverse__class_Odivide [219, 3] (w:1, o:251, a:1, s:1, b:0)
% 1.48/1.90 ,
% 1.48/1.90 c_Nat__Transfer_Otsub [220, 2] (w:1, o:227, a:1, s:1, b:0),
% 1.48/1.90 class_RealVector_Oreal__normed__field [221, 1] (w:1, o:148, a:1, s:1
% 1.48/1.90 , b:0),
% 1.48/1.90 class_Rings_Odivision__ring [222, 1] (w:1, o:149, a:1, s:1, b:0),
% 1.48/1.90 class_Rings_Odivision__ring__inverse__zero [223, 1] (w:1, o:150, a:1
% 1.48/1.90 , s:1, b:0),
% 1.48/1.90 class_Fields_Ofield__inverse__zero [224, 1] (w:1, o:117, a:1, s:1, b:
% 1.48/1.90 0),
% 1.48/1.90 class_Fields_Olinordered__field__inverse__zero [225, 1] (w:1, o:118
% 1.48/1.90 , a:1, s:1, b:0),
% 1.48/1.90 class_Fields_Olinordered__field [226, 1] (w:1, o:119, a:1, s:1, b:0)
% 1.48/1.90 ,
% 1.48/1.90 class_RealVector_Oreal__field [227, 1] (w:1, o:151, a:1, s:1, b:0),
% 1.48/1.90 c_Divides_Odiv__class_Omod [228, 3] (w:1, o:252, a:1, s:1, b:0),
% 1.48/1.90 class_Divides_Oring__div [229, 1] (w:1, o:183, a:1, s:1, b:0),
% 1.48/1.90 class_Groups_Ocancel__comm__monoid__add [231, 1] (w:1, o:184, a:1, s:
% 1.48/1.90 1, b:0),
% 1.48/1.90 tc_HOL_Obool [233, 0] (w:1, o:84, a:1, s:1, b:0),
% 1.48/1.90 v_a [234, 0] (w:1, o:100, a:1, s:1, b:0),
% 1.48/1.90 alpha1 [235, 3] (w:1, o:253, a:1, s:1, b:1),
% 1.48/1.90 alpha2 [236, 3] (w:1, o:262, a:1, s:1, b:1),
% 1.48/1.90 alpha3 [237, 3] (w:1, o:271, a:1, s:1, b:1),
% 1.48/1.90 alpha4 [238, 2] (w:1, o:231, a:1, s:1, b:1),
% 1.48/1.90 alpha5 [239, 2] (w:1, o:232, a:1, s:1, b:1),
% 1.48/1.90 alpha6 [240, 4] (w:1, o:299, a:1, s:1, b:1),
% 1.48/1.90 alpha7 [241, 4] (w:1, o:301, a:1, s:1, b:1),
% 1.48/1.90 alpha8 [242, 2] (w:1, o:233, a:1, s:1, b:1),
% 1.48/1.90 alpha9 [243, 2] (w:1, o:234, a:1, s:1, b:1),
% 1.48/1.90 alpha10 [244, 2] (w:1, o:235, a:1, s:1, b:1),
% 1.48/1.90 alpha11 [245, 3] (w:1, o:254, a:1, s:1, b:1),
% 1.48/1.90 alpha12 [246, 3] (w:1, o:255, a:1, s:1, b:1),
% 1.48/1.90 alpha13 [247, 3] (w:1, o:256, a:1, s:1, b:1),
% 1.48/1.90 alpha14 [248, 3] (w:1, o:257, a:1, s:1, b:1),
% 1.48/1.90 alpha15 [249, 2] (w:1, o:236, a:1, s:1, b:1),
% 1.48/1.90 alpha16 [250, 3] (w:1, o:258, a:1, s:1, b:1),
% 1.48/1.90 alpha17 [251, 3] (w:1, o:259, a:1, s:1, b:1),
% 1.48/1.90 alpha18 [252, 3] (w:1, o:260, a:1, s:1, b:1),
% 1.48/1.90 alpha19 [253, 3] (w:1, o:261, a:1, s:1, b:1),
% 1.48/1.90 alpha20 [254, 3] (w:1, o:263, a:1, s:1, b:1),
% 1.48/1.90 alpha21 [255, 3] (w:1, o:264, a:1, s:1, b:1),
% 14.33/14.72 alpha22 [256, 3] (w:1, o:265, a:1, s:1, b:1),
% 14.33/14.72 alpha23 [257, 3] (w:1, o:266, a:1, s:1, b:1),
% 14.33/14.72 alpha24 [258, 3] (w:1, o:267, a:1, s:1, b:1),
% 14.33/14.72 alpha25 [259, 3] (w:1, o:268, a:1, s:1, b:1),
% 14.33/14.72 alpha26 [260, 4] (w:1, o:302, a:1, s:1, b:1),
% 14.33/14.72 alpha27 [261, 3] (w:1, o:269, a:1, s:1, b:1),
% 14.33/14.72 alpha28 [262, 3] (w:1, o:270, a:1, s:1, b:1),
% 14.33/14.72 alpha29 [263, 4] (w:1, o:303, a:1, s:1, b:1),
% 14.33/14.72 alpha30 [264, 4] (w:1, o:304, a:1, s:1, b:1),
% 14.33/14.72 alpha31 [265, 2] (w:1, o:228, a:1, s:1, b:1),
% 14.33/14.72 alpha32 [266, 2] (w:1, o:229, a:1, s:1, b:1),
% 14.33/14.72 alpha33 [267, 3] (w:1, o:272, a:1, s:1, b:1),
% 14.33/14.72 alpha34 [268, 3] (w:1, o:273, a:1, s:1, b:1),
% 14.33/14.72 alpha35 [269, 3] (w:1, o:274, a:1, s:1, b:1),
% 14.33/14.72 alpha36 [270, 2] (w:1, o:230, a:1, s:1, b:1),
% 14.33/14.72 alpha37 [271, 4] (w:1, o:305, a:1, s:1, b:1),
% 14.33/14.72 alpha38 [272, 4] (w:1, o:306, a:1, s:1, b:1),
% 14.33/14.72 alpha39 [273, 3] (w:1, o:275, a:1, s:1, b:1),
% 14.33/14.72 alpha40 [274, 3] (w:1, o:276, a:1, s:1, b:1),
% 14.33/14.72 alpha41 [275, 3] (w:1, o:277, a:1, s:1, b:1),
% 14.33/14.72 alpha42 [276, 3] (w:1, o:278, a:1, s:1, b:1),
% 14.33/14.72 alpha43 [277, 4] (w:1, o:307, a:1, s:1, b:1),
% 14.33/14.72 alpha44 [278, 4] (w:1, o:308, a:1, s:1, b:1),
% 14.33/14.72 alpha45 [279, 4] (w:1, o:309, a:1, s:1, b:1),
% 14.33/14.72 alpha46 [280, 4] (w:1, o:310, a:1, s:1, b:1),
% 14.33/14.72 alpha47 [281, 4] (w:1, o:311, a:1, s:1, b:1),
% 14.33/14.72 alpha48 [282, 3] (w:1, o:279, a:1, s:1, b:1),
% 14.33/14.72 alpha49 [283, 4] (w:1, o:312, a:1, s:1, b:1),
% 14.33/14.72 alpha50 [284, 4] (w:1, o:289, a:1, s:1, b:1),
% 14.33/14.72 alpha51 [285, 4] (w:1, o:290, a:1, s:1, b:1),
% 14.33/14.72 alpha52 [286, 4] (w:1, o:291, a:1, s:1, b:1),
% 14.33/14.72 alpha53 [287, 4] (w:1, o:292, a:1, s:1, b:1),
% 14.33/14.72 alpha54 [288, 4] (w:1, o:293, a:1, s:1, b:1),
% 14.33/14.72 alpha55 [289, 4] (w:1, o:294, a:1, s:1, b:1),
% 14.33/14.72 alpha56 [290, 4] (w:1, o:295, a:1, s:1, b:1),
% 14.33/14.72 alpha57 [291, 4] (w:1, o:296, a:1, s:1, b:1),
% 14.33/14.72 alpha58 [292, 4] (w:1, o:297, a:1, s:1, b:1),
% 14.33/14.72 alpha59 [293, 4] (w:1, o:298, a:1, s:1, b:1),
% 14.33/14.72 alpha60 [294, 4] (w:1, o:300, a:1, s:1, b:1),
% 14.33/14.72 alpha61 [295, 3] (w:1, o:280, a:1, s:1, b:1),
% 14.33/14.72 alpha62 [296, 3] (w:1, o:281, a:1, s:1, b:1),
% 14.33/14.72 skol1 [297, 2] (w:1, o:214, a:1, s:1, b:1),
% 14.33/14.72 skol2 [298, 3] (w:1, o:285, a:1, s:1, b:1),
% 14.33/14.72 skol3 [299, 2] (w:1, o:215, a:1, s:1, b:1),
% 14.33/14.72 skol4 [300, 3] (w:1, o:286, a:1, s:1, b:1),
% 14.33/14.72 skol5 [301, 3] (w:1, o:287, a:1, s:1, b:1),
% 14.33/14.72 skol6 [302, 1] (w:1, o:106, a:1, s:1, b:1),
% 14.33/14.72 skol7 [303, 2] (w:1, o:216, a:1, s:1, b:1),
% 14.33/14.72 skol8 [304, 2] (w:1, o:217, a:1, s:1, b:1),
% 14.33/14.72 skol9 [305, 2] (w:1, o:218, a:1, s:1, b:1),
% 14.33/14.72 skol10 [306, 2] (w:1, o:219, a:1, s:1, b:1),
% 14.33/14.72 skol11 [307, 2] (w:1, o:220, a:1, s:1, b:1),
% 14.33/14.72 skol12 [308, 3] (w:1, o:282, a:1, s:1, b:1),
% 14.33/14.72 skol13 [309, 3] (w:1, o:283, a:1, s:1, b:1),
% 14.33/14.72 skol14 [310, 2] (w:1, o:221, a:1, s:1, b:1),
% 14.33/14.72 skol15 [311, 2] (w:1, o:222, a:1, s:1, b:1),
% 14.33/14.72 skol16 [312, 1] (w:1, o:107, a:1, s:1, b:1),
% 14.33/14.72 skol17 [313, 3] (w:1, o:284, a:1, s:1, b:1),
% 14.33/14.72 skol18 [314, 1] (w:1, o:108, a:1, s:1, b:1).
% 14.33/14.72
% 14.33/14.72
% 14.33/14.72 Starting Search:
% 14.33/14.72
% 14.33/14.72 *** allocated 113905 integers for clauses
% 14.33/14.72 *** allocated 170857 integers for clauses
% 14.33/14.72 Resimplifying inuse:
% 14.33/14.72 Done
% 14.33/14.72
% 14.33/14.72
% 14.33/14.72 Intermediate Status:
% 14.33/14.72 Generated: 3628
% 14.33/14.72 Kept: 2102
% 14.33/14.72 Inuse: 31
% 14.33/14.72 Deleted: 0
% 14.33/14.72 Deletedinuse: 0
% 14.33/14.72
% 14.33/14.72 *** allocated 256285 integers for clauses
% 14.33/14.72 *** allocated 170857 integers for termspace/termends
% 14.33/14.72 Resimplifying inuse:
% 14.33/14.72 Done
% 14.33/14.72
% 14.33/14.72 Resimplifying inuse:
% 14.33/14.72 Done
% 14.33/14.72
% 14.33/14.72
% 14.33/14.72 Intermediate Status:
% 14.33/14.72 Generated: 7625
% 14.33/14.72 Kept: 4102
% 14.33/14.72 Inuse: 135
% 14.33/14.72 Deleted: 2
% 14.33/14.72 Deletedinuse: 0
% 14.33/14.72
% 14.33/14.72 *** allocated 384427 integers for clauses
% 14.33/14.72 Resimplifying inuse:
% 14.33/14.72 Done
% 14.33/14.72
% 14.33/14.72 *** allocated 256285 integers for termspace/termends
% 14.33/14.72 Resimplifying inuse:
% 14.33/14.72 Done
% 14.33/14.72
% 14.33/14.72
% 14.33/14.72 Intermediate Status:
% 14.33/14.72 Generated: 12710
% 14.33/14.72 Kept: 6423
% 14.33/14.72 Inuse: 189
% 14.33/14.72 Deleted: 2
% 14.33/14.72 Deletedinuse: 0
% 14.33/14.72
% 14.33/14.72 Resimplifying inuse:
% 14.33/14.72 Done
% 14.33/14.72
% 14.33/14.72 *** allocated 576640 integers for clauses
% 14.33/14.72 Resimplifying inuse:
% 14.33/14.72 Done
% 14.33/14.72
% 14.33/14.72
% 14.33/14.72 Intermediate Status:
% 14.33/14.72 Generated: 17349
% 14.33/14.72 Kept: 8441
% 14.33/14.72 Inuse: 235
% 14.33/14.72 Deleted: 2
% 14.33/14.72 Deletedinuse: 0
% 14.33/14.72
% 14.33/14.72 *** allocated 384427 integers for termspace/termends
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98
% 51.58/51.98 Intermediate Status:
% 51.58/51.98 Generated: 25193
% 51.58/51.98 Kept: 11060
% 51.58/51.98 Inuse: 284
% 51.58/51.98 Deleted: 2
% 51.58/51.98 Deletedinuse: 0
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98 *** allocated 864960 integers for clauses
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98
% 51.58/51.98 Intermediate Status:
% 51.58/51.98 Generated: 33136
% 51.58/51.98 Kept: 13135
% 51.58/51.98 Inuse: 319
% 51.58/51.98 Deleted: 2
% 51.58/51.98 Deletedinuse: 0
% 51.58/51.98
% 51.58/51.98 *** allocated 576640 integers for termspace/termends
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98
% 51.58/51.98 Intermediate Status:
% 51.58/51.98 Generated: 38600
% 51.58/51.98 Kept: 15177
% 51.58/51.98 Inuse: 363
% 51.58/51.98 Deleted: 3
% 51.58/51.98 Deletedinuse: 0
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98 *** allocated 1297440 integers for clauses
% 51.58/51.98
% 51.58/51.98 Intermediate Status:
% 51.58/51.98 Generated: 55779
% 51.58/51.98 Kept: 18614
% 51.58/51.98 Inuse: 403
% 51.58/51.98 Deleted: 3
% 51.58/51.98 Deletedinuse: 0
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98 *** allocated 864960 integers for termspace/termends
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98 Resimplifying clauses:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98
% 51.58/51.98 Intermediate Status:
% 51.58/51.98 Generated: 63351
% 51.58/51.98 Kept: 20638
% 51.58/51.98 Inuse: 441
% 51.58/51.98 Deleted: 217
% 51.58/51.98 Deletedinuse: 0
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98
% 51.58/51.98 Intermediate Status:
% 51.58/51.98 Generated: 79523
% 51.58/51.98 Kept: 22747
% 51.58/51.98 Inuse: 463
% 51.58/51.98 Deleted: 217
% 51.58/51.98 Deletedinuse: 0
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98
% 51.58/51.98 Intermediate Status:
% 51.58/51.98 Generated: 85607
% 51.58/51.98 Kept: 24775
% 51.58/51.98 Inuse: 491
% 51.58/51.98 Deleted: 217
% 51.58/51.98 Deletedinuse: 0
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98
% 51.58/51.98 Intermediate Status:
% 51.58/51.98 Generated: 93325
% 51.58/51.98 Kept: 26786
% 51.58/51.98 Inuse: 521
% 51.58/51.98 Deleted: 217
% 51.58/51.98 Deletedinuse: 0
% 51.58/51.98
% 51.58/51.98 *** allocated 1946160 integers for clauses
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98 *** allocated 1297440 integers for termspace/termends
% 51.58/51.98
% 51.58/51.98 Intermediate Status:
% 51.58/51.98 Generated: 100985
% 51.58/51.98 Kept: 29611
% 51.58/51.98 Inuse: 548
% 51.58/51.98 Deleted: 217
% 51.58/51.98 Deletedinuse: 0
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98
% 51.58/51.98 Intermediate Status:
% 51.58/51.98 Generated: 109328
% 51.58/51.98 Kept: 32419
% 51.58/51.98 Inuse: 563
% 51.58/51.98 Deleted: 217
% 51.58/51.98 Deletedinuse: 0
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98
% 51.58/51.98 Intermediate Status:
% 51.58/51.98 Generated: 118955
% 51.58/51.98 Kept: 34559
% 51.58/51.98 Inuse: 593
% 51.58/51.98 Deleted: 217
% 51.58/51.98 Deletedinuse: 0
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98
% 51.58/51.98 Intermediate Status:
% 51.58/51.98 Generated: 129392
% 51.58/51.98 Kept: 36632
% 51.58/51.98 Inuse: 638
% 51.58/51.98 Deleted: 217
% 51.58/51.98 Deletedinuse: 0
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98
% 51.58/51.98 Intermediate Status:
% 51.58/51.98 Generated: 139432
% 51.58/51.98 Kept: 38781
% 51.58/51.98 Inuse: 662
% 51.58/51.98 Deleted: 218
% 51.58/51.98 Deletedinuse: 0
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98 Resimplifying clauses:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98
% 51.58/51.98 Intermediate Status:
% 51.58/51.98 Generated: 151880
% 51.58/51.98 Kept: 41570
% 51.58/51.98 Inuse: 672
% 51.58/51.98 Deleted: 302
% 51.58/51.98 Deletedinuse: 0
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98 *** allocated 2919240 integers for clauses
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98 *** allocated 1946160 integers for termspace/termends
% 51.58/51.98
% 51.58/51.98 Intermediate Status:
% 51.58/51.98 Generated: 165052
% 51.58/51.98 Kept: 44399
% 51.58/51.98 Inuse: 702
% 51.58/51.98 Deleted: 302
% 51.58/51.98 Deletedinuse: 0
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98
% 51.58/51.98 Intermediate Status:
% 51.58/51.98 Generated: 174094
% 51.58/51.98 Kept: 46721
% 51.58/51.98 Inuse: 707
% 51.58/51.98 Deleted: 302
% 51.58/51.98 Deletedinuse: 0
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98
% 51.58/51.98 Intermediate Status:
% 51.58/51.98 Generated: 186848
% 51.58/51.98 Kept: 49206
% 51.58/51.98 Inuse: 747
% 51.58/51.98 Deleted: 302
% 51.58/51.98 Deletedinuse: 0
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98
% 51.58/51.98 Intermediate Status:
% 51.58/51.98 Generated: 197802
% 51.58/51.98 Kept: 51243
% 51.58/51.98 Inuse: 787
% 51.58/51.98 Deleted: 303
% 51.58/51.98 Deletedinuse: 1
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98
% 51.58/51.98 Intermediate Status:
% 51.58/51.98 Generated: 205468
% 51.58/51.98 Kept: 53321
% 51.58/51.98 Inuse: 822
% 51.58/51.98 Deleted: 303
% 51.58/51.98 Deletedinuse: 1
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98
% 51.58/51.98 Intermediate Status:
% 51.58/51.98 Generated: 211550
% 51.58/51.98 Kept: 57161
% 51.58/51.98 Inuse: 827
% 51.58/51.98 Deleted: 303
% 51.58/51.98 Deletedinuse: 1
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98
% 51.58/51.98 Intermediate Status:
% 51.58/51.98 Generated: 220174
% 51.58/51.98 Kept: 59857
% 51.58/51.98 Inuse: 842
% 51.58/51.98 Deleted: 303
% 51.58/51.98 Deletedinuse: 1
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98 Resimplifying clauses:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98
% 51.58/51.98 Intermediate Status:
% 51.58/51.98 Generated: 228834
% 51.58/51.98 Kept: 61969
% 51.58/51.98 Inuse: 872
% 51.58/51.98 Deleted: 616
% 51.58/51.98 Deletedinuse: 1
% 51.58/51.98
% 51.58/51.98 Resimplifying inuse:
% 51.58/51.98 Done
% 51.58/51.98
% 51.58/51.98 *** allocated 4378860 integers for clauses
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 235117
% 130.07/130.49 Kept: 64063
% 130.07/130.49 Inuse: 892
% 130.07/130.49 Deleted: 616
% 130.07/130.49 Deletedinuse: 1
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49 *** allocated 2919240 integers for termspace/termends
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 240326
% 130.07/130.49 Kept: 66844
% 130.07/130.49 Inuse: 902
% 130.07/130.49 Deleted: 616
% 130.07/130.49 Deletedinuse: 1
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 250249
% 130.07/130.49 Kept: 68883
% 130.07/130.49 Inuse: 930
% 130.07/130.49 Deleted: 617
% 130.07/130.49 Deletedinuse: 2
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 254123
% 130.07/130.49 Kept: 71165
% 130.07/130.49 Inuse: 932
% 130.07/130.49 Deleted: 617
% 130.07/130.49 Deletedinuse: 2
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 258538
% 130.07/130.49 Kept: 73564
% 130.07/130.49 Inuse: 937
% 130.07/130.49 Deleted: 617
% 130.07/130.49 Deletedinuse: 2
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 264788
% 130.07/130.49 Kept: 75581
% 130.07/130.49 Inuse: 976
% 130.07/130.49 Deleted: 617
% 130.07/130.49 Deletedinuse: 2
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 269508
% 130.07/130.49 Kept: 78104
% 130.07/130.49 Inuse: 982
% 130.07/130.49 Deleted: 617
% 130.07/130.49 Deletedinuse: 2
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 284670
% 130.07/130.49 Kept: 80266
% 130.07/130.49 Inuse: 987
% 130.07/130.49 Deleted: 617
% 130.07/130.49 Deletedinuse: 2
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49 Resimplifying clauses:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 295926
% 130.07/130.49 Kept: 82939
% 130.07/130.49 Inuse: 1002
% 130.07/130.49 Deleted: 872
% 130.07/130.49 Deletedinuse: 2
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 308534
% 130.07/130.49 Kept: 85383
% 130.07/130.49 Inuse: 1027
% 130.07/130.49 Deleted: 872
% 130.07/130.49 Deletedinuse: 2
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 320338
% 130.07/130.49 Kept: 88662
% 130.07/130.49 Inuse: 1052
% 130.07/130.49 Deleted: 872
% 130.07/130.49 Deletedinuse: 2
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 332101
% 130.07/130.49 Kept: 91591
% 130.07/130.49 Inuse: 1067
% 130.07/130.49 Deleted: 872
% 130.07/130.49 Deletedinuse: 2
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 342684
% 130.07/130.49 Kept: 93670
% 130.07/130.49 Inuse: 1102
% 130.07/130.49 Deleted: 872
% 130.07/130.49 Deletedinuse: 2
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49 *** allocated 6568290 integers for clauses
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 363361
% 130.07/130.49 Kept: 98227
% 130.07/130.49 Inuse: 1142
% 130.07/130.49 Deleted: 872
% 130.07/130.49 Deletedinuse: 2
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 376416
% 130.07/130.49 Kept: 101284
% 130.07/130.49 Inuse: 1152
% 130.07/130.49 Deleted: 872
% 130.07/130.49 Deletedinuse: 2
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49 Resimplifying clauses:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 389851
% 130.07/130.49 Kept: 103357
% 130.07/130.49 Inuse: 1197
% 130.07/130.49 Deleted: 949
% 130.07/130.49 Deletedinuse: 2
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 398444
% 130.07/130.49 Kept: 106841
% 130.07/130.49 Inuse: 1212
% 130.07/130.49 Deleted: 949
% 130.07/130.49 Deletedinuse: 2
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49 *** allocated 4378860 integers for termspace/termends
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 405742
% 130.07/130.49 Kept: 110027
% 130.07/130.49 Inuse: 1222
% 130.07/130.49 Deleted: 949
% 130.07/130.49 Deletedinuse: 2
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 433603
% 130.07/130.49 Kept: 113946
% 130.07/130.49 Inuse: 1237
% 130.07/130.49 Deleted: 949
% 130.07/130.49 Deletedinuse: 2
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 447133
% 130.07/130.49 Kept: 116050
% 130.07/130.49 Inuse: 1261
% 130.07/130.49 Deleted: 950
% 130.07/130.49 Deletedinuse: 2
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 451489
% 130.07/130.49 Kept: 118178
% 130.07/130.49 Inuse: 1272
% 130.07/130.49 Deleted: 995
% 130.07/130.49 Deletedinuse: 3
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 457145
% 130.07/130.49 Kept: 120202
% 130.07/130.49 Inuse: 1275
% 130.07/130.49 Deleted: 1007
% 130.07/130.49 Deletedinuse: 3
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 470175
% 130.07/130.49 Kept: 122563
% 130.07/130.49 Inuse: 1283
% 130.07/130.49 Deleted: 1019
% 130.07/130.49 Deletedinuse: 3
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49 Resimplifying clauses:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 486736
% 130.07/130.49 Kept: 125673
% 130.07/130.49 Inuse: 1293
% 130.07/130.49 Deleted: 1333
% 130.07/130.49 Deletedinuse: 4
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 130.07/130.49 Generated: 495151
% 130.07/130.49 Kept: 127732
% 130.07/130.49 Inuse: 1313
% 130.07/130.49 Deleted: 1333
% 130.07/130.49 Deletedinuse: 4
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49 Resimplifying inuse:
% 130.07/130.49 Done
% 130.07/130.49
% 130.07/130.49
% 130.07/130.49 Intermediate Status:
% 281.02/281.52 Generated: 501404
% 281.02/281.52 Kept: 129734
% 281.02/281.52 Inuse: 1349
% 281.02/281.52 Deleted: 1333
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 507937
% 281.02/281.52 Kept: 131793
% 281.02/281.52 Inuse: 1378
% 281.02/281.52 Deleted: 1333
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 516062
% 281.02/281.52 Kept: 133846
% 281.02/281.52 Inuse: 1408
% 281.02/281.52 Deleted: 1333
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 524872
% 281.02/281.52 Kept: 135899
% 281.02/281.52 Inuse: 1427
% 281.02/281.52 Deleted: 1333
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 533141
% 281.02/281.52 Kept: 138004
% 281.02/281.52 Inuse: 1438
% 281.02/281.52 Deleted: 1333
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 550627
% 281.02/281.52 Kept: 140661
% 281.02/281.52 Inuse: 1453
% 281.02/281.52 Deleted: 1333
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52 Resimplifying clauses:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 561167
% 281.02/281.52 Kept: 142704
% 281.02/281.52 Inuse: 1471
% 281.02/281.52 Deleted: 1496
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 572377
% 281.02/281.52 Kept: 144892
% 281.02/281.52 Inuse: 1478
% 281.02/281.52 Deleted: 1496
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 583722
% 281.02/281.52 Kept: 146926
% 281.02/281.52 Inuse: 1486
% 281.02/281.52 Deleted: 1496
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 594576
% 281.02/281.52 Kept: 148956
% 281.02/281.52 Inuse: 1503
% 281.02/281.52 Deleted: 1496
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52 *** allocated 9852435 integers for clauses
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 609384
% 281.02/281.52 Kept: 152967
% 281.02/281.52 Inuse: 1528
% 281.02/281.52 Deleted: 1496
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 621651
% 281.02/281.52 Kept: 154972
% 281.02/281.52 Inuse: 1552
% 281.02/281.52 Deleted: 1496
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 *** allocated 6568290 integers for termspace/termends
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 632370
% 281.02/281.52 Kept: 157848
% 281.02/281.52 Inuse: 1558
% 281.02/281.52 Deleted: 1496
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 641988
% 281.02/281.52 Kept: 160100
% 281.02/281.52 Inuse: 1563
% 281.02/281.52 Deleted: 1496
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 683866
% 281.02/281.52 Kept: 164744
% 281.02/281.52 Inuse: 1578
% 281.02/281.52 Deleted: 1496
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52 Resimplifying clauses:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 721185
% 281.02/281.52 Kept: 168534
% 281.02/281.52 Inuse: 1588
% 281.02/281.52 Deleted: 1595
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 747765
% 281.02/281.52 Kept: 172155
% 281.02/281.52 Inuse: 1598
% 281.02/281.52 Deleted: 1595
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 755511
% 281.02/281.52 Kept: 174257
% 281.02/281.52 Inuse: 1614
% 281.02/281.52 Deleted: 1595
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 765202
% 281.02/281.52 Kept: 179037
% 281.02/281.52 Inuse: 1623
% 281.02/281.52 Deleted: 1595
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 773772
% 281.02/281.52 Kept: 181731
% 281.02/281.52 Inuse: 1638
% 281.02/281.52 Deleted: 1595
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 790539
% 281.02/281.52 Kept: 185062
% 281.02/281.52 Inuse: 1653
% 281.02/281.52 Deleted: 1595
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52 Resimplifying clauses:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 798524
% 281.02/281.52 Kept: 189130
% 281.02/281.52 Inuse: 1658
% 281.02/281.52 Deleted: 1909
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 809361
% 281.02/281.52 Kept: 192776
% 281.02/281.52 Inuse: 1668
% 281.02/281.52 Deleted: 1909
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 817427
% 281.02/281.52 Kept: 195775
% 281.02/281.52 Inuse: 1673
% 281.02/281.52 Deleted: 1909
% 281.02/281.52 Deletedinuse: 4
% 281.02/281.52
% 281.02/281.52 Resimplifying inuse:
% 281.02/281.52 Done
% 281.02/281.52
% 281.02/281.52
% 281.02/281.52 Intermediate Status:
% 281.02/281.52 Generated: 826585
% 281.02/281.52 Kept: 19931Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------