TSTP Solution File: SWW182+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW182+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.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 23:21:05 EDT 2022
% Result : Timeout 300.02s 300.44s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW182+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n020.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 : Sun Jun 5 18:38:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.95/1.59 *** allocated 10000 integers for termspace/termends
% 0.95/1.59 *** allocated 10000 integers for clauses
% 0.95/1.59 *** allocated 10000 integers for justifications
% 0.95/1.59 *** allocated 15000 integers for termspace/termends
% 0.95/1.59 *** allocated 22500 integers for termspace/termends
% 0.95/1.59 *** allocated 33750 integers for termspace/termends
% 0.95/1.59 Bliksem 1.12
% 0.95/1.59
% 0.95/1.59
% 0.95/1.59 Automatic Strategy Selection
% 0.95/1.59
% 0.95/1.59 *** allocated 50625 integers for termspace/termends
% 0.95/1.59 *** allocated 75937 integers for termspace/termends
% 0.95/1.59 *** allocated 113905 integers for termspace/termends
% 0.95/1.59
% 0.95/1.59 Clauses:
% 0.95/1.59
% 0.95/1.59 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.95/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.59 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.95/1.59 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.95/1.59 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.95/1.59 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.95/1.59 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.95/1.59 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.95/1.59 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.95/1.59 , hAPP( hAPP( c_fequal, Y ), c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ) ), U, c_Polynomial_Opoly__rec( W, X, U, T, Y )
% 0.95/1.59 ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.95/1.59 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.59 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ),
% 0.95/1.59 c_Polynomial_OpCons( X, Z, Y ) ) ), hBOOL( hAPP( hAPP(
% 0.95/1.59 c_HOL_Oequal__class_Oequal( X ), c_Groups_Ozero__class_Ozero( X ) ), Z )
% 0.95/1.59 ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.59 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ),
% 0.95/1.59 c_Polynomial_OpCons( X, Z, Y ) ) ), hBOOL( hAPP( hAPP(
% 0.95/1.59 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.59 c_HOL_Oequal__class_Oequal( X ), c_Groups_Ozero__class_Ozero( X ) ), Z )
% 0.95/1.59 ), ! hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly
% 0.95/1.59 ( X ) ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) )
% 0.95/1.59 , hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X )
% 0.95/1.59 ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ),
% 0.95/1.59 c_Polynomial_OpCons( X, Z, Y ) ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.59 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.95/1.59 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ) ) ), hBOOL( hAPP( hAPP(
% 0.95/1.59 c_HOL_Oequal__class_Oequal( X ), Z ), c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.59 ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.59 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.95/1.59 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ) ) ), hBOOL( hAPP( hAPP(
% 0.95/1.59 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ), Y ),
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.59 c_HOL_Oequal__class_Oequal( X ), Z ), c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.59 ), ! hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly
% 0.95/1.59 ( X ) ), Y ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) )
% 0.95/1.59 , hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X )
% 0.95/1.59 ), c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ) ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero
% 0.95/1.59 ( tc_Polynomial_Opoly( X ) ) ) ), hBOOL( hAPP( Y, skol2( Z, Y ) ) ),
% 0.95/1.59 hBOOL( hAPP( Y, T ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero
% 0.95/1.59 ( tc_Polynomial_Opoly( X ) ) ) ), ! hBOOL( hAPP( Y, c_Polynomial_OpCons(
% 0.95/1.59 X, skol25( X, Y ), skol2( X, Y ) ) ) ), hBOOL( hAPP( Y, Z ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.59 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), Z = Y
% 0.95/1.59 }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! Z = Y, hBOOL( hAPP
% 0.95/1.59 ( hAPP( c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 0.95/1.59 ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.95/1.59 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.95/1.59 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.59 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.95/1.59 c_Polynomial_OpCons( X, U, T ) ), c_Polynomial_OpCons( X, Z, Y ) ) ),
% 0.95/1.59 hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal( X ), U ), Z ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.59 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.95/1.59 c_Polynomial_OpCons( X, U, T ) ), c_Polynomial_OpCons( X, Z, Y ) ) ),
% 0.95/1.59 hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) )
% 0.95/1.59 , T ), Y ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP(
% 0.95/1.59 c_HOL_Oequal__class_Oequal( X ), U ), Z ) ), ! hBOOL( hAPP( hAPP(
% 0.95/1.59 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ), T ), Y ) ), hBOOL
% 0.95/1.59 ( hAPP( hAPP( c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.95/1.59 c_Polynomial_OpCons( X, U, T ) ), c_Polynomial_OpCons( X, Z, Y ) ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 0.95/1.59 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), hBOOL( hAPP( hAPP(
% 0.95/1.59 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ) ),
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ),
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.59 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.59 { ! class_HOL_Oequal( X ), c_HOL_Oequal__class_Oequal( X ) = c_fequal }.
% 0.95/1.59 { ! class_HOL_Oequal( X ), hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal( X
% 0.95/1.59 ), Y ), Y ) ) }.
% 0.95/1.59 { ! class_HOL_Oequal( X ), ! hBOOL( hAPP( hAPP( c_HOL_Oequal__class_Oequal
% 0.95/1.59 ( X ), Z ), Y ) ), Z = Y }.
% 0.95/1.59 { ! class_HOL_Oequal( X ), ! Z = Y, hBOOL( hAPP( hAPP(
% 0.95/1.59 c_HOL_Oequal__class_Oequal( X ), Z ), Y ) ) }.
% 0.95/1.59 { ! class_HOL_Oequal( X ), c_fequal = c_HOL_Oequal__class_Oequal( X ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 0.95/1.59 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.59 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 0.95/1.59 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.59 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.59 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.59 }.
% 0.95/1.59 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.59 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.59 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.59 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 0.95/1.59 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol3( X
% 0.95/1.59 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol3( X, Y, Z ) ), Z = Y
% 0.95/1.59 }.
% 0.95/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.95/1.59 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.95/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.95/1.59 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 0.95/1.59 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 0.95/1.59 c_Polynomial_Ocoeff( X, Y ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.59 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.95/1.59 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.59 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 0.95/1.59 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.95/1.59 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.95/1.59 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.95/1.59 ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.59 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Nat_Onat ) ) = Z }.
% 0.95/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.95/1.59 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.59 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.59 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.95/1.59 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.95/1.59 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.95/1.59 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 0.95/1.59 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 0.95/1.59 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 0.95/1.59 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 0.95/1.59 , Y ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.95/1.59 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.95/1.59 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 0.95/1.59 }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.95/1.59 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.95/1.59 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 0.95/1.59 ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_Ocoeff( X, c_Polynomial_OpCons( X
% 0.95/1.59 , Z, Y ) ) = c_Nat_Onat_Onat__case( X, Z, c_Polynomial_Ocoeff( X, Y ) ) }
% 0.95/1.59 .
% 0.95/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.59 Y, T ), Z = Y }.
% 0.95/1.59 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.59 T, Y ), Z = Y }.
% 0.95/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.59 T, Y ), Z = Y }.
% 0.95/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.59 Y, Z ), T = Y }.
% 0.95/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.59 Y, Z ) }.
% 0.95/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.59 T, Y ), Z = Y }.
% 0.95/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.59 T, Y ) }.
% 0.95/1.59 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.95/1.59 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.95/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.95/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.95/1.59 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.95/1.59 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.95/1.59 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 0.95/1.59 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.95/1.59 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.95/1.59 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.95/1.59 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.95/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.95/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.95/1.59 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.95/1.59 { hAPP( c_Nat_Onat_Onat__case( Z, Y, X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Nat_Onat ) ) = Y }.
% 0.95/1.59 { hAPP( c_Nat_Onat_Onat__case( T, Z, Y ), c_Nat_OSuc( X ) ) = hAPP( Y, X )
% 0.95/1.59 }.
% 0.95/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.59 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.95/1.59 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.95/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.95/1.59 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.95/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.95/1.59 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.95/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.95/1.59 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.95/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.95/1.59 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 0.95/1.59 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.95/1.59 { ! X = c_Nat_OSuc( X ) }.
% 0.95/1.59 { ! c_Nat_OSuc( X ) = X }.
% 0.95/1.59 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.95/1.59 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.95/1.59 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.95/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.95/1.59 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.95/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 0.95/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 0.95/1.59 c_Polynomial_OpCons( X, T,
% 0.95/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 0.95/1.59 .
% 0.95/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.59 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.95/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.59 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.59 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.59 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X, Z, Y ) =
% 0.95/1.59 c_Polynomial_OAbs__poly( X, c_Nat_Onat_Onat__case( X, Z,
% 0.95/1.59 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.95/1.59 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.95/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.95/1.59 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.95/1.59 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.95/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.95/1.59 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 0.95/1.59 .
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.95/1.59 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.95/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 0.95/1.59 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 0.95/1.59 .
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.95/1.59 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.95/1.59 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.59 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.95/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.95/1.59 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.95/1.59 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.95/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.95/1.59 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.95/1.59 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.95/1.59 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.59 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.95/1.59 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 0.95/1.59 c_Polynomial_Odegree( X, Z ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.95/1.59 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.95/1.59 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.95/1.59 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 0.95/1.59 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.95/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.95/1.59 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.95/1.59 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.95/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.59 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.95/1.59 ), U = Z, T = Y }.
% 0.95/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.59 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.95/1.59 ) }.
% 0.95/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.59 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.95/1.59 ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.95/1.59 ) ), Z ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.95/1.59 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.59 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.95/1.59 ) }.
% 0.95/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.59 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.95/1.59 ), ! U = T }.
% 0.95/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.59 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.95/1.59 ), ! Z = Y }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.59 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.95/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.95/1.59 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.95/1.59 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.95/1.59 ) }.
% 0.95/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Nat_Onat ), X ) = X }.
% 0.95/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.95/1.59 ( tc_Nat_Onat ) ) = X }.
% 0.95/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.95/1.59 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.95/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.95/1.59 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.95/1.59 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.95/1.59 .
% 0.95/1.59 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.95/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.95/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.95/1.59 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.95/1.59 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.95/1.59 .
% 0.95/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.95/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.95/1.59 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.95/1.59 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.95/1.59 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.59 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.95/1.59 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.59 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.59 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.95/1.59 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.95/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.59 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.95/1.59 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 0.95/1.59 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 0.95/1.59 .
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.95/1.59 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 0.95/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 0.95/1.59 ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.95/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.95/1.59 ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_OAbs__poly( X,
% 0.95/1.59 c_Polynomial_Ocoeff( X, Y ) ) = Y }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.59 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.95/1.59 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.95/1.59 ) }.
% 0.95/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.59 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.95/1.59 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.95/1.59 ) }.
% 0.95/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.59 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.59 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 0.95/1.59 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha1( X, Y ), alpha15
% 0.95/1.59 ( X, Y ) }.
% 0.95/1.59 { ! alpha1( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.59 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.95/1.59 { ! alpha15( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.59 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.95/1.59 { ! alpha15( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! alpha15( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Nat_Onat ) ) }.
% 0.95/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha15( X, Y ) }.
% 0.95/1.59 { ! alpha1( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Nat_Onat ) ) }.
% 0.95/1.59 { ! alpha1( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha1( X, Y ) }.
% 0.95/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha2( X, Y ), alpha16( X
% 0.95/1.59 , Y ) }.
% 0.95/1.59 { ! alpha2( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.59 { ! alpha16( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.59 { ! alpha16( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! alpha16( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Nat_Onat ) ) }.
% 0.95/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha16( X, Y ) }.
% 0.95/1.59 { ! alpha2( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Nat_Onat ) ) }.
% 0.95/1.59 { ! alpha2( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha2( X, Y ) }.
% 0.95/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.95/1.59 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.95/1.59 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.59 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.95/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.95/1.59 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 0.95/1.59 Y ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.59 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 0.95/1.59 ), Y ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.59 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.95/1.59 , Y ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.95/1.59 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.95/1.59 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.59 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.59 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.95/1.59 c_Polynomial_Odegree( X, Y ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.59 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.59 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.59 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 0.95/1.59 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.95/1.59 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 0.95/1.59 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.59 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.59 }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 0.95/1.59 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.95/1.59 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.95/1.59 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.95/1.59 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.95/1.59 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.95/1.59 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.95/1.59 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.95/1.59 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.95/1.59 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.95/1.59 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.95/1.59 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.59 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.95/1.59 ) ), T ), Y ) }.
% 0.95/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.95/1.59 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.95/1.59 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.95/1.59 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.59 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.59 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.59 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.59 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.59 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.95/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.95/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.95/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.95/1.59 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.59 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.95/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.95/1.59 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.95/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.95/1.59 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.95/1.59 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.59 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.95/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.95/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.95/1.59 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.95/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.95/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.95/1.59 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.95/1.59 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.95/1.59 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.95/1.59 .
% 0.95/1.59 { c_Nat_Onat_Onat__size( c_Nat_OSuc( X ) ) = c_Groups_Oplus__class_Oplus(
% 0.95/1.59 tc_Nat_Onat, c_Nat_Onat_Onat__size( X ), c_Nat_OSuc(
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.95/1.59 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_Osize__class_Osize(
% 0.95/1.59 tc_Nat_Onat, X ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.59 ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.95/1.59 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Opcompose( X, Z, Y )
% 0.95/1.59 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.59 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.95/1.59 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.59 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 0.95/1.59 ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.95/1.59 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 0.95/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ),
% 0.95/1.59 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.95/1.59 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.95/1.59 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.95/1.59 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.95/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.59 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.95/1.59 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.59 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.95/1.59 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.59 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.59 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.95/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.59 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.95/1.59 ) }.
% 0.95/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.59 { ! class_Rings_Olinordered__semidom( X ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.59 c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.59 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 0.95/1.59 ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.95/1.59 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.95/1.59 ) }.
% 0.95/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.95/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.95/1.59 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.59 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.95/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.95/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.95/1.59 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.95/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.95/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.95/1.59 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.95/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.59 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.95/1.59 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.95/1.59 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.59 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.95/1.59 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.59 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.95/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.95/1.59 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.95/1.59 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.59 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.95/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.59 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.95/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.59 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.95/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.59 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.95/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.59 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.95/1.59 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.95/1.59 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.95/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.59 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.59 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.59 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.59 { c_Nat_Osize__class_Osize( tc_Nat_Onat, X ) = X }.
% 0.95/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.95/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.95/1.59 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.95/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.95/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.95/1.59 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.95/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.59 ) }.
% 0.95/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.59 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.95/1.59 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.59 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.59 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.59 ) }.
% 0.95/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.95/1.59 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.59 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.95/1.59 ( X, Y ), Y ) }.
% 0.95/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.95/1.59 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.95/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.95/1.59 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.95/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.95/1.59 = Y }.
% 0.95/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.59 ) }.
% 0.95/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.95/1.59 ( X ) }.
% 0.95/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.59 , Y ) }.
% 0.95/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.59 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.95/1.59 ) }.
% 0.95/1.59 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.95/1.59 ) }.
% 0.95/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.59 = Y }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.95/1.59 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ) ) }.
% 0.95/1.59 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.95/1.59 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.95/1.59 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.95/1.59 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.95/1.59 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.95/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.95/1.59 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.95/1.59 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.95/1.59 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.95/1.59 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.59 ( X, Y ) ) }.
% 0.95/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.59 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.59 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.59 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.59 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.59 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.95/1.59 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.59 ) ), Y ) }.
% 0.95/1.59 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.95/1.59 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.59 ( X, Y ) ) }.
% 0.95/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.95/1.59 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.95/1.59 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.59 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.59 Y ) ) = Y }.
% 0.95/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.59 Z, Y ) ) = Y }.
% 0.95/1.59 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.59 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.95/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.95/1.59 = Y }.
% 0.95/1.59 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.95/1.59 = Y }.
% 0.95/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.95/1.59 = Y }.
% 0.95/1.59 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.95/1.59 = Y }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.95/1.59 = Y }.
% 0.95/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.95/1.59 = Y }.
% 0.95/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.59 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.95/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.59 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.59 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.59 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.95/1.59 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.59 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.95/1.59 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.59 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.95/1.59 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.59 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.95/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.59 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.59 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.95/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.59 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Nat_Onat ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.95/1.59 ) }.
% 0.95/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.95/1.59 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.95/1.59 }.
% 0.95/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.95/1.59 c_Nat_OSuc( X ) ) }.
% 0.95/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.95/1.59 ) }.
% 0.95/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.59 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.95/1.59 , c_Nat_OSuc( X ) ) }.
% 0.95/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.95/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.95/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.95/1.59 .
% 0.95/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.95/1.59 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol4( X, Y ) ) }.
% 0.95/1.60 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.95/1.60 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.95/1.60 c_Polynomial_Odegree( X, Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.95/1.60 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.95/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.95/1.60 tc_Nat_Onat ) }.
% 0.95/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.95/1.60 tc_Nat_Onat ) }.
% 0.95/1.60 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.95/1.60 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.60 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.60 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.95/1.60 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.95/1.60 , Y ), X ) }.
% 0.95/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 0.95/1.60 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.95/1.60 { c_Nat_Onat_Onat__size( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.95/1.60 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.60 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.95/1.60 ), Y ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 0.95/1.60 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.95/1.60 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.60 Z ) = Y }.
% 0.95/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.60 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.95/1.60 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.95/1.60 ( X, Y ) }.
% 0.95/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 X ) }.
% 0.95/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__semiring( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__semiring( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__semiring( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__semiring( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ) ), alpha3( X, Y, Z ), alpha17( X, Y, Z ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha17( X, Y, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ) ) }.
% 0.95/1.60 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ), Y ), alpha17( X, Y, Z ) }.
% 0.95/1.60 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.60 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ), alpha3( X, Y, Z ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha4( X, Y
% 0.95/1.60 , Z ), alpha18( X, Y, Z ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha18( X, Y, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.60 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ), alpha18( X, Y, Z ) }.
% 0.95/1.60 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.60 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), alpha4( X, Y, Z ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.60 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 Z, Y ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 Y, Z ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.95/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.95/1.60 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.95/1.60 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ) }.
% 0.95/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.60 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.60 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.95/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.95/1.60 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.60 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.95/1.60 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.95/1.60 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.95/1.60 ), X ) ) }.
% 0.95/1.60 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.95/1.60 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.95/1.60 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.95/1.60 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.95/1.60 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) )
% 0.95/1.60 , c_Polynomial_Odegree( X, Y ) ) }.
% 0.95/1.60 { ! class_Groups_Ocomm__monoid__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.95/1.60 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.60 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.95/1.60 , c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Z, Y ) ), Y ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.60 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.95/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.60 tc_Nat_Onat, Y, c_Polynomial_Odegree( X, Z ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.95/1.60 , c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Z, Y ) ), c_Nat_OSuc(
% 0.95/1.60 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.95/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.95/1.60 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.95/1.60 ( X, Z ) }.
% 0.95/1.60 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.60 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.95/1.60 , Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol5( X, Y ) ) }.
% 0.95/1.60 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.60 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.60 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.60 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.60 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.60 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.60 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.60 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.95/1.60 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.60 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.95/1.60 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.95/1.60 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.95/1.60 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z,
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.95/1.60 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 0.95/1.60 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.95/1.60 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 0.95/1.60 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 0.95/1.60 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 0.95/1.60 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.95/1.60 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.95/1.60 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.95/1.60 hAPP( Y, U ) ) }.
% 0.95/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.95/1.60 ( Z, skol6( X, Y, Z ) ), hAPP( Y, skol6( X, Y, Z ) ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.95/1.60 ( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.95/1.60 ( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.95/1.60 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.95/1.60 hAPP( Y, U ) ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.60 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.95/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.95/1.60 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.95/1.60 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.95/1.60 hAPP( Y, U ) ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.60 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.95/1.60 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.95/1.60 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.95/1.60 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.60 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.95/1.60 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.95/1.60 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.95/1.60 ) ) }.
% 0.95/1.60 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.95/1.60 ( X, Y ), Z = Y }.
% 0.95/1.60 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.95/1.60 ( X, Y ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.95/1.60 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.95/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 X ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 0.95/1.60 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.95/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.95/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.95/1.60 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.95/1.60 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 0.95/1.60 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.95/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), ! hAPP(
% 0.95/1.60 c_Polynomial_Ocoeff( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 0.95/1.60 , Y ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.95/1.60 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 0.95/1.60 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 0.95/1.60 { c_HOL_Obool_Obool__size( c_fFalse ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.95/1.60 X ) ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.95/1.60 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Z ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.95/1.60 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Y ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.60 Y ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.95/1.60 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 Y ), ! Z = Y }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.60 Z ), ! Z = Y }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.60 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.60 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.60 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.95/1.60 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.60 , ! Z = Y }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.60 , ! Z = Y }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.60 , ! Y = Z }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.95/1.60 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.95/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.95/1.60 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.60 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.60 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.60 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.95/1.60 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.60 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.60 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.60 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.60 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.60 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.95/1.60 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.95/1.60 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.95/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 0.95/1.60 X, Y ) ) = Y }.
% 0.95/1.60 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.60 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ) }.
% 0.95/1.60 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.60 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.60 = Y }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.95/1.60 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 0.95/1.60 , Z, Y ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.95/1.60 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 0.95/1.60 ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.95/1.60 , Y ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.95/1.60 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.95/1.60 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.95/1.60 ) }.
% 0.95/1.60 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.60 , Y ) ) = Y }.
% 0.95/1.60 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.95/1.60 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, Y, Z ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.60 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.95/1.60 Z, T ) }.
% 0.95/1.60 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.95/1.60 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.95/1.60 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.95/1.60 { alpha37( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.95/1.60 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.95/1.60 { alpha37( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.95/1.60 ( X, Y ), Z ) ) }.
% 0.95/1.60 { ! alpha37( X, Y, Z ), alpha40( X, Y, Z ), Z = Y }.
% 0.95/1.60 { ! alpha37( X, Y, Z ), alpha40( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.95/1.60 ) ) }.
% 0.95/1.60 { ! alpha40( X, Y, Z ), alpha37( X, Y, Z ) }.
% 0.95/1.60 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha37( X, Y, Z ) }.
% 0.95/1.60 { ! alpha40( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.95/1.60 }.
% 0.95/1.60 { ! alpha40( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.95/1.60 X, Y ), Z ) ), alpha40( X, Y, Z ) }.
% 0.95/1.60 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.60 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.60 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.60 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.60 , ! Z = Y }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.60 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.95/1.60 ( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.60 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.60 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.60 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.95/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.60 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.60 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.60 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.95/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, T, Y ) }.
% 0.95/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.60 , Y, Z ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.95/1.60 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, Z, Y ) }.
% 0.95/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.60 , T, Y ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.60 , Y, T ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.60 , T, Y ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.60 , T ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.95/1.60 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, Z, Y ) }.
% 0.95/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.95/1.60 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, Z, Y ) }.
% 0.95/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.60 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.60 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.95/1.60 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.95/1.60 ( X, Y ), Z ) }.
% 0.95/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.60 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.95/1.60 ( X, Z ), Y ) }.
% 0.95/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.95/1.60 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.95/1.60 .
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), X ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.95/1.60 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.95/1.60 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.95/1.60 .
% 0.95/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.95/1.60 .
% 0.95/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.95/1.60 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.95/1.60 X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.60 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.95/1.60 }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.60 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.95/1.60 , X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.95/1.60 .
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.95/1.60 .
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.60 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.95/1.60 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.95/1.60 .
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.60 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.60 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), T, Z ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), T, Y ), c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), Z, T ), c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Opoly__gcd( X, Y, T ) ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.95/1.60 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.95/1.60 }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.95/1.60 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.95/1.60 }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.95/1.60 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.95/1.60 }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.95/1.60 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.95/1.60 }.
% 0.95/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 0.95/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.95/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.60 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.95/1.60 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 0.95/1.60 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 0.95/1.60 X, T, Z ), Y ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.95/1.60 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.95/1.60 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.95/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.95/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha5( X, Y, Z, T ),
% 0.95/1.60 alpha19( X, Y, Z, T ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z, T ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha19( X, Y, Z, T ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.60 { ! alpha19( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! alpha19( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha19( X, Y, Z, T ) }.
% 0.95/1.60 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.95/1.60 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.95/1.60 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha5( X, Y, Z, T ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha6( X, Y, Z, T ),
% 0.95/1.60 alpha20( X, Y, Z, T ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z, T ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha20( X, Y, Z, T ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! alpha20( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! alpha20( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha20( X, Y, Z, T ) }.
% 0.95/1.60 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.60 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.60 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha6( X, Y, Z, T ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.60 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.95/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.95/1.60 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.95/1.60 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.95/1.60 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.95/1.60 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.95/1.60 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.60 , Y, T ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.95/1.60 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.60 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.60 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.95/1.60 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.60 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.60 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.60 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 , Y ) }.
% 0.95/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.60 , Y ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.95/1.60 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol7( X ) ) }.
% 0.95/1.60 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha7( X, Y ) }.
% 0.95/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.60 { ! alpha7( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.60 c_Nat_OSuc( X ) ) }.
% 0.95/1.60 { ! alpha7( X, Y ), Y = c_Nat_OSuc( skol8( Z, Y ) ) }.
% 0.95/1.60 { ! alpha7( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol8( X, Y
% 0.95/1.60 ), X ) }.
% 0.95/1.60 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.95/1.60 ), alpha7( X, Y ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.95/1.60 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.60 c_Polynomial_Odegree( X, Y ) ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), Y, Z ), Z = Y }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol9( X, Y ) ) ) }.
% 0.95/1.60 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.95/1.60 .
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.95/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.60 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.60 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.60 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.60 tc_Nat_Onat ), X ), Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), Z ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.95/1.60 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.95/1.60 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.60 Y ), X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.95/1.60 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.95/1.60 ), X ) ) }.
% 0.95/1.60 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.95/1.60 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.95/1.60 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.95/1.60 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.95/1.60 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.60 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.95/1.60 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.95/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.95/1.60 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.95/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.95/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 0.95/1.60 ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.60 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.60 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.95/1.60 ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.95/1.60 ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.60 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.95/1.60 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha8( X
% 0.95/1.60 , Y, T ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha21( X
% 0.95/1.60 , Y, Z, T ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! alpha8( X, Y, T ), ! alpha21( X, Y, Z, T )
% 0.95/1.60 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 0.95/1.60 ( X, T, Z ), Y ) }.
% 0.95/1.60 { ! alpha21( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.95/1.60 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha21( X, Y, Z, T ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha21( X
% 0.95/1.60 , Y, Z, T ) }.
% 0.95/1.60 { ! alpha8( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { Z = c_Groups_Ozero__class_Ozero( X ), alpha8( X, Y, Z ) }.
% 0.95/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha8( X
% 0.95/1.60 , Y, Z ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.95/1.60 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.95/1.60 ( X ), Z, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X )
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree
% 0.95/1.60 ( X, Z ), c_Polynomial_Odegree( X, Y ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.95/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.95/1.60 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.95/1.60 ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.95/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.95/1.60 ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.95/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.60 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 0.95/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.95/1.60 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.95/1.60 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.95/1.60 { c_HOL_Obool_Obool__size( c_fTrue ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.95/1.60 }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 0.95/1.60 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.95/1.60 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.60 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.95/1.60 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.95/1.60 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.95/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.95/1.60 ) ) }.
% 0.95/1.60 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.95/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.95/1.60 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.95/1.60 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.95/1.60 }.
% 0.95/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.95/1.60 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 0.95/1.60 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.60 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.60 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.95/1.60 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.60 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.95/1.60 X ) ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.95/1.60 ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 0.95/1.60 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.95/1.60 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 0.95/1.60 , Y = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.60 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 0.95/1.60 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 0.95/1.60 = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.60 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ) ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.95/1.60 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.95/1.60 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.95/1.60 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.60 , Y ) ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.60 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ) ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.60 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.60 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.60 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.60 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.95/1.60 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 0.95/1.60 , Y ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.95/1.60 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse
% 0.95/1.60 ( X, Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.95/1.60 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.60 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.95/1.60 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.95/1.60 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.95/1.60 hAPP( Z, skol10( U, W, Z ) ) ) }.
% 0.95/1.60 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.95/1.60 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol10( X
% 0.95/1.60 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.95/1.60 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 0.95/1.60 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol26( X,
% 0.95/1.60 Y, Z ) ) ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), Z, Y ), alpha41( X, Y, Z, T ), ! Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), Z, Y ), alpha41( X, Y, Z, T ), ! hAPP(
% 0.95/1.60 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.95/1.60 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 0.95/1.60 .
% 0.95/1.60 { ! alpha41( X, Y, Z, T ), alpha42( X, Y, Z, T ), alpha38( X, Y, T ) }.
% 0.95/1.60 { ! alpha41( X, Y, Z, T ), alpha42( X, Y, Z, T ), ! hAPP(
% 0.95/1.60 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! alpha42( X, Y, Z, T ), alpha41( X, Y, Z, T ) }.
% 0.95/1.60 { ! alpha38( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.95/1.60 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 alpha41( X, Y, Z, T ) }.
% 0.95/1.60 { ! alpha42( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.95/1.60 ( X ), Z, T ), alpha43( X, Y, Z, T ) }.
% 0.95/1.60 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, T ), alpha42( X, Y
% 0.95/1.60 , Z, T ) }.
% 0.95/1.60 { ! alpha43( X, Y, Z, T ), alpha42( X, Y, Z, T ) }.
% 0.95/1.60 { ! alpha43( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.95/1.60 ), skol11( X, Y, U, W ), Y ) }.
% 0.95/1.60 { ! alpha43( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.95/1.60 ), skol11( X, Y, U, T ), T ) }.
% 0.95/1.60 { ! alpha43( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.95/1.60 ( X ), skol11( X, Y, Z, T ), Z ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Y ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, T ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Z ), alpha43( X, Y
% 0.95/1.60 , Z, T ) }.
% 0.95/1.60 { ! alpha38( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! alpha38( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha38( X, Y, Z
% 0.95/1.60 ) }.
% 0.95/1.60 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 0.95/1.60 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha9( X, Y ), Y = X }
% 0.95/1.60 .
% 0.95/1.60 { ! alpha9( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! alpha9( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! alpha9( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Nat_Onat, X, Y ), alpha9( X, Y ) }.
% 0.95/1.60 { ! alpha10( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! alpha10( X, Y ), ! Y = X }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha10( X, Y ) }
% 0.95/1.60 .
% 0.95/1.60 { ! alpha10( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! alpha10( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Nat_Onat, X, Y ), alpha10( X, Y ) }.
% 0.95/1.60 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.95/1.60 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Nat_Onat, Y, X ), Y = X }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.95/1.60 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Nat_Onat, Y, Z ) }.
% 0.95/1.60 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Nat_Onat, Y, Z ) }.
% 0.95/1.60 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 0.95/1.60 , Z ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 0.95/1.60 Z, Y ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Nat_Onat, Y, Z ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), Y ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.95/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.95/1.60 Y ) ) ), Y ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.95/1.60 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 0.95/1.60 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.60 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.95/1.60 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.95/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.95/1.60 Y ) ) ), Y ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.95/1.60 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.95/1.60 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.95/1.60 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.95/1.60 tc_Nat_Onat ) ) = Y }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Nat_Onat, Z, Y ) ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.95/1.60 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.60 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.95/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.95/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.95/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.95/1.60 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Orderings_Oord__class_Oless__eq
% 0.95/1.60 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 0.95/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.60 c_Polynomial_Odegree( X, Z ) ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.95/1.60 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.95/1.60 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 0.95/1.60 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.95/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.95/1.60 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.95/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 0.95/1.60 ( X ) }.
% 0.95/1.60 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.95/1.60 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 0.95/1.60 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.60 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.95/1.60 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.95/1.60 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ) ) }.
% 0.95/1.60 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.95/1.60 tc_Nat_Onat ), X ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.60 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.60 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.60 ( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.95/1.60 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.95/1.60 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Nat_Onat, Z, X ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Int_Oint, Z, X ) }.
% 0.95/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 0.95/1.60 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 0.95/1.60 ) }.
% 0.95/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.95/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 0.95/1.60 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.95/1.60 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.95/1.60 ), X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.95/1.60 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.95/1.60 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.60 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.95/1.60 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.60 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.60 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.95/1.60 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.95/1.60 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.60 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.95/1.60 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.95/1.60 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), Y ) }.
% 0.95/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.95/1.60 ), X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.95/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.95/1.60 ) }.
% 0.95/1.60 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( X ) }.
% 0.95/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.60 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.95/1.60 = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.60 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.95/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.95/1.60 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 0.95/1.60 ) ), Y ) }.
% 0.95/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.95/1.60 tc_Nat_Onat ) ) = Y }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.60 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.95/1.60 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.95/1.60 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.95/1.60 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.95/1.60 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.95/1.60 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Nat_Onat ) }.
% 0.95/1.60 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.95/1.60 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.95/1.60 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.95/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.95/1.60 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.60 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.95/1.60 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.95/1.60 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.95/1.60 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.60 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.95/1.60 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.95/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.60 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.95/1.60 ) ), Z ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.95/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.95/1.60 ), T ), U ), Y ) }.
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.60 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.95/1.60 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.95/1.60 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.95/1.60 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.60 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 X ), Y ), Z = Y }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.95/1.60 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.60 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.60 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.60 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.95/1.60 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.95/1.60 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.60 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.95/1.60 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.95/1.60 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.60 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.95/1.60 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.95/1.60 c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.60 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.95/1.60 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.60 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.95/1.60 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.60 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.95/1.60 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 0.95/1.60 }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.95/1.60 , alpha25( X, Y, Z, T ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha25( X, Y, Z, T ),
% 0.95/1.60 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 0.95/1.60 { ! alpha25( X, Y, Z, T ), alpha11( X, Z, T ) }.
% 0.95/1.60 { ! alpha25( X, Y, Z, T ), alpha22( X, Y, T ) }.
% 0.95/1.60 { ! alpha11( X, Z, T ), ! alpha22( X, Y, T ), alpha25( X, Y, Z, T ) }.
% 0.95/1.60 { ! alpha22( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), alpha26( X, Y, Z ) }.
% 0.95/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha22( X
% 0.95/1.60 , Y, Z ) }.
% 0.95/1.60 { ! alpha26( X, Y, Z ), alpha22( X, Y, Z ) }.
% 0.95/1.60 { ! alpha26( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.60 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 0.95/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha26( X
% 0.95/1.60 , Y, Z ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 0.95/1.60 ), c_Polynomial_Odegree( X, Z ) ), alpha26( X, Y, Z ) }.
% 0.95/1.60 { ! alpha11( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha11( X,
% 0.95/1.60 Y, Z ) }.
% 0.95/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha11( X
% 0.95/1.60 , Y, Z ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.95/1.60 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.60 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.60 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.60 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.60 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.95/1.60 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.95/1.60 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 0.95/1.60 .
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Int_Oint, Y, X ), X = Y }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.95/1.60 ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.95/1.60 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 0.95/1.60 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.95/1.60 , Z ), X ) ), T ) ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Int_Oint, U, T ) ) }.
% 0.95/1.60 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Int_Oint, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.95/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.95/1.60 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 0.95/1.60 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 0.95/1.60 ) ) }.
% 0.95/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 0.95/1.60 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.95/1.60 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.95/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.95/1.60 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.95/1.60 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.95/1.60 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.95/1.60 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 0.95/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.95/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.95/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.95/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.95/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.95/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.95/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.95/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.95/1.60 , c_Polynomial_Opdivmod__rel( X, c_Polynomial_Osmult( X, W, U ), T,
% 0.95/1.60 c_Polynomial_Osmult( X, W, Z ), c_Polynomial_Osmult( X, W, Y ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 0.95/1.60 .
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.95/1.60 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.95/1.60 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.95/1.60 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.95/1.60 .
% 0.95/1.60 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.95/1.60 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.95/1.60 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.95/1.60 ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.95/1.60 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 0.95/1.60 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 0.95/1.60 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.95/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 0.95/1.60 ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.95/1.60 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.95/1.60 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.95/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.95/1.60 c_Polynomial_Opdivmod__rel( X, W, U, T, Z ), c_Polynomial_Opdivmod__rel(
% 0.95/1.60 X, W, c_Polynomial_Osmult( X, Y, U ), c_Polynomial_Osmult( X,
% 0.95/1.60 c_Rings_Oinverse__class_Oinverse( X, Y ), T ), Z ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.95/1.60 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.95/1.60 alpha12( X, Y, Z ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.95/1.60 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.95/1.60 { ! class_Rings_Olinordered__idom( X ), ! alpha12( X, Y, Z ),
% 0.95/1.60 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.95/1.60 { ! alpha12( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.60 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.95/1.60 alpha12( X, Y, Z ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.95/1.60 , skol12( T, U, Z ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.60 c_Polynomial_Odegree( X, Y ), Z ) }.
% 0.95/1.60 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ), skol12( X
% 0.95/1.60 , Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.95/1.60 Y ), Z ) }.
% 0.95/1.60 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.95/1.60 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol13( Z, Y
% 0.95/1.60 ), Y ) }.
% 0.95/1.60 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.95/1.60 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.95/1.60 skol13( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.95/1.60 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.95/1.60 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.95/1.60 , skol13( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.95/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.95/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.60 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.95/1.60 ( tc_Int_Oint ) }.
% 0.95/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Int_Oint ), X ) = X }.
% 0.95/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Int_Oint ) ) = X }.
% 0.95/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.95/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.95/1.60 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.95/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.95/1.60 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.95/1.60 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.95/1.60 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.95/1.60 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.95/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.95/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.95/1.60 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.95/1.60 .
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Int_Oint ), X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.60 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.95/1.60 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.60 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.60 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.95/1.60 .
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.95/1.60 tc_Int_Oint ) ), X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.95/1.60 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.95/1.60 }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.95/1.60 tc_Int_Oint ) ), X ) }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.60 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.95/1.60 = X }.
% 0.95/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Int_Oint ) ) ) }.
% 0.95/1.61 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Int_Oint ) ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.95/1.61 }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Int_Oint ) ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.95/1.61 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.95/1.61 ( tc_Int_Oint ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.95/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.95/1.61 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.95/1.61 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.61 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.95/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.95/1.61 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.95/1.61 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.95/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.95/1.61 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.95/1.61 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Int_Oint ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Int_Oint ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Int_Oint, X, Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol14( Z, Y ) ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.95/1.61 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Int_Oint, skol14( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.61 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.95/1.61 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 0.95/1.61 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 0.95/1.61 ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 0.95/1.61 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 0.95/1.61 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 0.95/1.61 c_Polynomial_Opoly__gcd( X, Z, c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T,
% 0.95/1.61 c_Polynomial_Osmult( X, Y, Z ) ) = c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.95/1.61 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), Y ) ) = c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.95/1.61 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.95/1.61 ( X ), Z, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.95/1.61 c_Polynomial_Opoly__gcd( X, Y, c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 0.95/1.61 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.95/1.61 , c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, T,
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, Z, Y ) ), ! c_Rings_Odvd__class_Odvd( X, T
% 0.95/1.61 , Y ), c_Rings_Odvd__class_Odvd( X, T, Z ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.95/1.61 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 0.95/1.61 , c_Divides_Odiv__class_Omod( X, Y, T ) ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.95/1.61 ), c_Divides_Odiv__class_Omod( X, c_Divides_Odiv__class_Omod( X, T, Y )
% 0.95/1.61 , Z ) = c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.95/1.61 ), ! c_Rings_Odvd__class_Odvd( X, Z, c_Divides_Odiv__class_Omod( X, T, Y
% 0.95/1.61 ) ), c_Rings_Odvd__class_Odvd( X, Z, T ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.95/1.61 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 0.95/1.61 , c_Divides_Odiv__class_Omod( X, T, Y ) ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 0.95/1.61 , Y ) ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.95/1.61 ), Z ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 0.95/1.61 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.95/1.61 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.95/1.61 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 0.95/1.61 X, Z, Y ) }.
% 0.95/1.61 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.95/1.61 = c_Divides_Odiv__class_Omod( X, Y, Z ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, T ), Z ) = c_Divides_Odiv__class_Omod
% 0.95/1.61 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.95/1.61 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.95/1.61 ( X, c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Omod( X, Z
% 0.95/1.61 , Y ) ), Y ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.95/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 0.95/1.61 ( X, Z, Y ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.95/1.61 ( X, Y, Z ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.95/1.61 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 0.95/1.61 , Y ) ), Y ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.95/1.61 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.95/1.61 ), Z ), Y ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.95/1.61 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.95/1.61 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.95/1.61 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 T, Z ), Y ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 0.95/1.61 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 T, Y ), Z ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.95/1.61 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.95/1.61 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 0.95/1.61 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 0.95/1.61 ), Z ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.95/1.61 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.95/1.61 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 X ) }.
% 0.95/1.61 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 0.95/1.61 Z ) = c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Polynomial_Opoly( X ), Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Polynomial_Odegree( X, c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.95/1.61 ( X ), Z, Y ) ), c_Polynomial_Odegree( X, Y ) ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.61 skol15( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, skol15( X, T, U ),
% 0.95/1.61 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.61 , Y ) }.
% 0.95/1.61 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), skol15( X, Y, Z ) ), Z ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.61 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 Z, c_Polynomial_Odegree( X, Y ) ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 tc_Nat_Onat, Z, skol16( T, U, Z ) ) }.
% 0.95/1.61 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 Z, c_Polynomial_Odegree( X, Y ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.95/1.61 skol16( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 0.95/1.61 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 0.95/1.61 }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.95/1.61 tc_Int_Oint, Y, c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.95/1.61 ( tc_Int_Oint, Y, X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( tc_Int_Oint, Y ), X ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.95/1.61 ( tc_Int_Oint, Y, X ) ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.95/1.61 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) ) }
% 0.95/1.61 .
% 0.95/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Int_Oint, X, Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.95/1.61 ( tc_Int_Oint, Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 0.95/1.61 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.95/1.61 c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.61 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol17( X, Y ) ) }.
% 0.95/1.61 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 0.95/1.61 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 0.95/1.61 ), Y ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 0.95/1.61 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol18( X, Y ) ) }.
% 0.95/1.61 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 0.95/1.61 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.95/1.61 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) ), Y ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.95/1.61 ( tc_Int_Oint, Y, X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Int_Oint, Y, X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Int_Oint, Y, X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, T, X ) ), Z ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.95/1.61 alpha13( X, Y, Z ) }.
% 0.95/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.95/1.61 alpha23( X, Y, Z ) }.
% 0.95/1.61 { ! alpha13( X, Y, Z ), ! alpha23( X, Y, Z ), hBOOL( hAPP( Z,
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ) }.
% 0.95/1.61 { ! alpha23( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.61 alpha27( X, Y, Z ) }.
% 0.95/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha23( X, Y, Z ) }.
% 0.95/1.61 { ! alpha27( X, Y, Z ), alpha23( X, Y, Z ) }.
% 0.95/1.61 { ! alpha27( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.95/1.61 ), alpha29( X, Y, Z, T ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol19( X, T, U ), X ),
% 0.95/1.61 alpha27( X, Y, Z ) }.
% 0.95/1.61 { ! alpha29( X, Y, Z, skol19( X, Y, Z ) ), alpha27( X, Y, Z ) }.
% 0.95/1.61 { ! alpha29( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.95/1.61 hBOOL( hAPP( Z, T ) ) }.
% 0.95/1.61 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol20( X, Y, T ) ), T
% 0.95/1.61 ), alpha29( X, Y, Z, T ) }.
% 0.95/1.61 { ! hBOOL( hAPP( Z, T ) ), alpha29( X, Y, Z, T ) }.
% 0.95/1.61 { ! alpha13( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.61 hBOOL( hAPP( Z, Y ) ) }.
% 0.95/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha13( X, Y, Z ) }.
% 0.95/1.61 { ! hBOOL( hAPP( Z, Y ) ), alpha13( X, Y, Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.95/1.61 tc_Nat_Onat ), X ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X )
% 0.95/1.61 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Omod
% 0.95/1.61 ( tc_Int_Oint, X, Y ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y )
% 0.95/1.61 }.
% 0.95/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 0.95/1.61 alpha14( X, Y, Z ) }.
% 0.95/1.61 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 0.95/1.61 alpha24( X, Y, Z ) }.
% 0.95/1.61 { ! alpha14( X, Y, Z ), ! alpha24( X, Y, Z ), hBOOL( hAPP( Z,
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.95/1.61 { ! alpha24( X, Y, Z ), alpha28( X, Y, Z ) }.
% 0.95/1.61 { ! alpha24( X, Y, Z ), alpha30( X, Y, Z ) }.
% 0.95/1.61 { ! alpha28( X, Y, Z ), ! alpha30( X, Y, Z ), alpha24( X, Y, Z ) }.
% 0.95/1.61 { ! alpha30( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha32( X, Y, Z ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha30( X, Y, Z ) }.
% 0.95/1.61 { ! alpha32( X, Y, Z ), alpha30( X, Y, Z ) }.
% 0.95/1.61 { ! alpha32( X, Y, Z ), ! alpha34( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.95/1.61 { ! hBOOL( hAPP( Z, skol21( T, U, Z ) ) ), alpha32( X, Y, Z ) }.
% 0.95/1.61 { alpha34( X, Y, skol21( X, Y, Z ) ), alpha32( X, Y, Z ) }.
% 0.95/1.61 { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z )
% 0.95/1.61 }.
% 0.95/1.61 { ! alpha34( X, Y, Z ), alpha36( X, Y, Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), ! alpha36( X, Y, Z
% 0.95/1.61 ), alpha34( X, Y, Z ) }.
% 0.95/1.61 { ! alpha36( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.61 { ! alpha36( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol22( X, Y,
% 0.95/1.61 Z ) ), Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha36( X,
% 0.95/1.61 Y, Z ) }.
% 0.95/1.61 { ! alpha28( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha31( X, Y, Z ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Int_Oint ), X ), alpha28( X, Y, Z ) }.
% 0.95/1.61 { ! alpha31( X, Y, Z ), alpha28( X, Y, Z ) }.
% 0.95/1.61 { ! alpha31( X, Y, Z ), ! alpha33( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.95/1.61 { ! hBOOL( hAPP( Z, skol23( T, U, Z ) ) ), alpha31( X, Y, Z ) }.
% 0.95/1.61 { alpha33( X, Y, skol23( X, Y, Z ) ), alpha31( X, Y, Z ) }.
% 0.95/1.61 { ! alpha33( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ) }.
% 0.95/1.61 { ! alpha33( X, Y, Z ), alpha35( X, Y, Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! alpha35( X, Y, Z ),
% 0.95/1.61 alpha33( X, Y, Z ) }.
% 0.95/1.61 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X )
% 0.95/1.61 }.
% 0.95/1.61 { ! alpha35( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol24( X, Y,
% 0.95/1.61 Z ) ), Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), ! Y =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha35( X,
% 0.95/1.61 Y, Z ) }.
% 0.95/1.61 { ! alpha14( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.95/1.61 hBOOL( hAPP( Z, Y ) ) }.
% 0.95/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha14( X, Y, Z ) }.
% 0.95/1.61 { ! hBOOL( hAPP( Z, Y ) ), alpha14( X, Y, Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.95/1.61 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.95/1.61 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 0.95/1.61 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ),
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.61 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha39( X,
% 0.95/1.61 Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Int_Oint, Z, Y ) = X }.
% 0.95/1.61 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha39( X,
% 0.95/1.61 Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.95/1.61 tc_Int_Oint, Z, Y ) = X }.
% 0.95/1.61 { ! alpha39( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.95/1.61 { ! alpha39( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha39( X, Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.95/1.61 , alpha39( X, Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3mod( X, Y ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3mod( X, Y ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Int_Oint, X,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.61 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.95/1.61 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.95/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.95/1.61 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.95/1.61 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 0.95/1.61 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 0.95/1.61 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 0.95/1.61 , U ), Z ) }.
% 0.95/1.61 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 0.95/1.61 Y ) ), Y ) }.
% 0.95/1.61 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 0.95/1.61 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.95/1.61 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.95/1.61 tc_Nat_Onat, Y, X ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.95/1.61 tc_Nat_Onat, Y, X ), X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) =
% 0.95/1.61 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.95/1.61 tc_Nat_Onat, X, Y ), Y ) }.
% 0.95/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.95/1.61 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.95/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.95/1.61 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.95/1.61 X, W, Z ) ), U ), T ), Y ) }.
% 0.95/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), Z ), U ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( X, Z, W ) ), U ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.95/1.61 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.95/1.61 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.95/1.61 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.95/1.61 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.95/1.61 }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.95/1.61 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.95/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.95/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.95/1.61 }.
% 0.95/1.61 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.61 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 0.95/1.61 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.95/1.61 Y ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y )
% 0.95/1.61 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 0.95/1.61 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X )
% 0.95/1.61 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.95/1.61 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.61 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.95/1.61 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.95/1.61 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.95/1.61 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.95/1.61 W ) ), U ), Y ) }.
% 0.95/1.61 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.95/1.61 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), Z ), U ), Y ) }.
% 0.95/1.61 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.95/1.61 Z ) ), U ), T ) = Y }.
% 0.95/1.61 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.95/1.61 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), Z ), U ), Y ) }.
% 0.95/1.61 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.61 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.95/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.95/1.61 Z ) ), Y ) ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.95/1.61 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.61 , Y ) ) }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.95/1.61 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.95/1.61 X, Z, Y ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.95/1.61 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.95/1.61 X, Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.95/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.95/1.61 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Nat_Onat, Z, X ), Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.61 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.95/1.61 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.95/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.95/1.61 ) }.
% 0.95/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.95/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.95/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.95/1.61 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.95/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.61 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.95/1.61 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.95/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.95/1.61 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.95/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.95/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.95/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.95/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.95/1.61 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.95/1.61 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.95/1.61 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.95/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.95/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.95/1.61 X, Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.61 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.61 ( X ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.95/1.61 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.95/1.61 , Z, Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.95/1.61 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.95/1.61 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.95/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.95/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.61 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.95/1.61 ( X ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__add(
% 0.95/1.61 X ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Ocomm__monoid__add( X
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring( X ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Omonoid__add( X ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0( X ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero( X ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring( X ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Ozero( X ) }.
% 0.95/1.61 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.95/1.61 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { class_Enum_Oenum( tc_HOL_Obool ) }.
% 0.95/1.61 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.95/1.61 { ! class_Enum_Oenum( Y ), ! class_Enum_Oenum( X ), class_Enum_Oenum(
% 0.95/1.61 tc_fun( Y, X ) ) }.
% 0.95/1.61 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.95/1.61 ( tc_fun( Y, X ) ) }.
% 0.95/1.61 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.95/1.61 ) ) }.
% 0.95/1.61 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.95/1.61 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.95/1.61 { ! class_Enum_Oenum( Y ), ! class_HOL_Oequal( X ), class_HOL_Oequal(
% 0.95/1.61 tc_fun( Y, X ) ) }.
% 0.95/1.61 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.95/1.61 tc_Int_Oint ) }.
% 0.95/1.61 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.95/1.61 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.95/1.61 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.95/1.61 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.95/1.61 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.95/1.61 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.95/1.61 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.95/1.61 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.95/1.61 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.95/1.61 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.95/1.61 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.95/1.61 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.95/1.61 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.95/1.61 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.95/1.61 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.95/1.61 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.95/1.61 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.95/1.61 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.95/1.61 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.95/1.61 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.95/1.61 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.95/1.61 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.95/1.61 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.95/1.61 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.95/1.61 { class_Power_Opower( tc_Int_Oint ) }.
% 0.95/1.61 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.95/1.61 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.95/1.61 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.95/1.61 { class_HOL_Oequal( tc_Int_Oint ) }.
% 0.95/1.61 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.95/1.61 tc_Nat_Onat ) }.
% 0.95/1.61 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.95/1.61 { class_HOL_Oequal( tc_Nat_Onat ) }.
% 0.95/1.61 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.95/1.61 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.95/1.61 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.95/1.61 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.95/1.61 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.95/1.61 { class_HOL_Oequal( tc_HOL_Obool ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ),
% 0.95/1.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.61 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.95/1.61 ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.61 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.95/1.61 X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.61 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.95/1.61 ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.61 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.95/1.61 }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.61 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.61 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.61 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.61 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.95/1.61 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.61 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.61 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.61 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.61 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.95/1.61 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.95/1.61 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.95/1.61 ( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.95/1.61 ( tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 0.95/1.61 ( X ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.95/1.61 }.
% 0.95/1.61 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.95/1.61 ) ) }.
% 0.95/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.95/1.61 .
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), class_HOL_Oequal(
% 0.95/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.95/1.61 { ! hBOOL( hAPP( hAPP( c_fequal, Y ), X ) ), Y = X }.
% 0.95/1.61 { ! Y = X, hBOOL( hAPP( hAPP( c_fequal, Y ), X ) ) }.
% 0.95/1.61 { ! hBOOL( c_fFalse ) }.
% 0.95/1.61 { hBOOL( c_fTrue ) }.
% 0.95/1.61 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( t_a,
% 0.95/1.61 c_Polynomial_OpCons( t_a, v_a, c_Groups_Ozero__class_Ozero(
% 0.95/1.61 tc_Polynomial_Opoly( t_a ) ) ), v_h ) = c_Polynomial_OpCons( t_a, v_a,
% 0.95/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ) ) }.
% 0.95/1.61 { class_Rings_Ocomm__semiring__0( t_a ) }.
% 0.95/1.61
% 0.95/1.61 *** allocated 15000 integers for clauses
% 0.95/1.61 *** allocated 22500 integers for clauses
% 0.95/1.61 *** allocated 33750 integers for clauses
% 0.95/1.61 *** allocated 50625 integers for clauses
% 0.95/1.61 *** allocated 75937 integers for clauses
% 0.95/1.61 percentage equality = 0.263802, percentage horn = 0.900963
% 0.95/1.61 This is a problem with some equality
% 0.95/1.61
% 0.95/1.61
% 0.95/1.61
% 0.95/1.61 Options Used:
% 0.95/1.61
% 0.95/1.61 useres = 1
% 0.95/1.61 useparamod = 1
% 0.95/1.61 useeqrefl = 1
% 0.95/1.61 useeqfact = 1
% 0.95/1.61 usefactor = 1
% 0.95/1.61 usesimpsplitting = 0
% 0.95/1.61 usesimpdemod = 5
% 0.95/1.61 usesimpres = 3
% 0.95/1.61
% 0.95/1.61 resimpinuse = 1000
% 0.95/1.61 resimpclauses = 20000
% 0.95/1.61 substype = eqrewr
% 0.95/1.61 backwardsubs = 1
% 0.95/1.61 selectoldest = 5
% 0.95/1.61
% 0.95/1.61 litorderings [0] = split
% 0.95/1.61 litorderings [1] = extend the termordering, first sorting on arguments
% 0.95/1.61
% 0.95/1.61 termordering = kbo
% 0.95/1.61
% 0.95/1.61 litapriori = 0
% 0.95/1.61 termapriori = 1
% 0.95/1.61 litaposteriori = 0
% 0.95/1.61 termaposteriori = 0
% 0.95/1.61 demodaposteriori = 0
% 0.95/1.61 ordereqreflfact = 0
% 0.95/1.61
% 0.95/1.61 litselect = negord
% 0.95/1.61
% 0.95/1.61 maxweight = 15
% 0.95/1.61 maxdepth = 30000
% 0.95/1.61 maxlength = 115
% 0.95/1.61 maxnrvars = 195
% 0.95/1.61 excuselevel = 1
% 0.95/1.61 increasemaxweight = 1
% 0.95/1.61
% 0.95/1.61 maxselected = 10000000
% 0.95/1.61 maxnrclauses = 10000000
% 0.95/1.61
% 0.95/1.61 showgenerated = 0
% 0.95/1.61 showkept = 0
% 0.95/1.61 showselected = 0
% 0.95/1.61 showdeleted = 0
% 0.95/1.61 showresimp = 1
% 0.95/1.61 showstatus = 2000
% 0.95/1.61
% 0.95/1.61 prologoutput = 0
% 0.95/1.61 nrgoals = 5000000
% 0.95/1.61 totalproof = 1
% 0.95/1.61
% 0.95/1.61 Symbols occurring in the translation:
% 0.95/1.61
% 0.95/1.61 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.95/1.61 . [1, 2] (w:1, o:196, a:1, s:1, b:0),
% 0.95/1.61 ! [4, 1] (w:0, o:111, a:1, s:1, b:0),
% 0.95/1.61 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.95/1.61 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.95/1.61 hAPP [38, 2] (w:1, o:220, a:1, s:1, b:0),
% 0.95/1.61 class_Rings_Ocomm__semiring__0 [41, 1] (w:1, o:118, a:1, s:1, b:0),
% 0.95/1.61 tc_Polynomial_Opoly [42, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.95/1.61 c_Groups_Ozero__class_Ozero [43, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.95/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [44, 3] (w:1
% 0.95/1.61 , o:250, a:1, s:1, b:0),
% 0.95/1.61 class_Groups_Ozero [45, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.95/1.61 c_Polynomial_OpCons [46, 3] (w:1, o:254, a:1, s:1, b:0),
% 0.95/1.61 c_Polynomial_Opoly__rec [54, 5] (w:1, o:316, a:1, s:1, b:0),
% 0.95/1.61 c_fequal [56, 0] (w:1, o:39, a:1, s:1, b:0),
% 0.95/1.61 c_If [57, 4] (w:1, o:304, a:1, s:1, b:0),
% 0.95/1.61 class_HOL_Oequal [58, 1] (w:1, o:147, a:1, s:1, b:0),
% 0.95/1.61 c_HOL_Oequal__class_Oequal [59, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.95/1.61 hBOOL [60, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.95/1.61 c_Polynomial_Omonom [65, 3] (w:1, o:255, a:1, s:1, b:0),
% 0.95/1.61 tc_Nat_Onat [68, 0] (w:1, o:56, a:1, s:1, b:0),
% 0.95/1.61 c_Nat_OSuc [71, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.95/1.61 c_Polynomial_Opcompose [73, 3] (w:1, o:256, a:1, s:1, b:0),
% 0.95/1.61 c_Polynomial_Opoly [74, 2] (w:1, o:221, a:1, s:1, b:0),
% 0.95/1.61 c_Polynomial_Osynthetic__div [76, 3] (w:1, o:257, a:1, s:1, b:0),
% 0.95/1.61 c_Polynomial_Osmult [78, 3] (w:1, o:258, a:1, s:1, b:0),
% 0.95/1.61 c_Polynomial_Ocoeff [80, 2] (w:1, o:222, a:1, s:1, b:0),
% 0.95/1.61 class_Rings_Oidom [81, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.95/1.61 class_Int_Oring__char__0 [83, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.95/1.61 c_Polynomial_Oorder [84, 3] (w:1, o:253, a:1, s:1, b:0),
% 0.95/1.61 c_Groups_Oplus__class_Oplus [87, 3] (w:1, o:259, a:1, s:1, b:0),
% 0.95/1.61 c_Nat_Onat_Onat__case [89, 3] (w:1, o:260, a:1, s:1, b:0),
% 0.95/1.61 class_Groups_Ocancel__semigroup__add [91, 1] (w:1, o:128, a:1, s:1
% 0.95/1.61 , b:0),
% 0.95/1.61 class_Groups_Ocancel__ab__semigroup__add [92, 1] (w:1, o:129, a:1, s:
% 0.95/1.61 1, b:0),
% 0.95/1.61 class_Groups_Oab__semigroup__add [94, 1] (w:1, o:130, a:1, s:1, b:0)
% 0.95/1.61 ,
% 0.95/1.61 class_Groups_Ocomm__monoid__add [95, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.95/1.61
% 0.95/1.61 class_Groups_Omonoid__add [99, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.95/1.61 class_Groups_Olinordered__ab__group__add [100, 1] (w:1, o:132, a:1
% 0.95/1.61 , s:1, b:0),
% 0.95/1.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.95/1.61 103, 1] (w:1, o:183, a:1, s:1, b:0),
% 0.95/1.61 class_Rings_Ocomm__semiring__1 [104, 1] (w:1, o:155, a:1, s:1, b:0),
% 0.95/1.61
% 0.95/1.61 c_Polynomial_OAbs__poly [105, 2] (w:1, o:223, a:1, s:1, b:0),
% 0.95/1.61 c_Groups_Otimes__class_Otimes [106, 1] (w:1, o:148, a:1, s:1, b:0),
% 0.95/1.61 c_Polynomial_Odegree [107, 2] (w:1, o:224, a:1, s:1, b:0),
% 0.95/1.61 class_Groups_Oab__semigroup__mult [108, 1] (w:1, o:134, a:1, s:1, b:0
% 0.95/1.61 ),
% 0.95/1.61 class_Rings_Olinordered__ring__strict [119, 1] (w:1, o:156, a:1, s:1
% 0.95/1.61 , b:0),
% 0.95/1.61 class_Rings_Osemiring [121, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.95/1.61 class_RealVector_Oreal__normed__algebra [123, 1] (w:1, o:162, a:1, s:
% 0.95/1.61 1, b:0),
% 0.95/1.61 class_Rings_Ocomm__semiring [125, 1] (w:1, o:163, a:1, s:1, b:0),
% 0.95/1.61 class_Rings_Omult__zero [128, 1] (w:1, o:172, a:1, s:1, b:0),
% 0.95/1.61 class_Rings_Ono__zero__divisors [130, 1] (w:1, o:173, a:1, s:1, b:0)
% 0.95/1.61 ,
% 0.95/1.61 class_Rings_Oring__no__zero__divisors [131, 1] (w:1, o:157, a:1, s:1
% 0.95/1.61 , b:0),
% 0.95/1.61 c_Nat_Onat_Onat__size [136, 1] (w:1, o:184, a:1, s:1, b:0),
% 0.95/1.61 c_Nat_Osize__class_Osize [137, 2] (w:1, o:225, a:1, s:1, b:0),
% 0.95/1.61 c_Orderings_Oord__class_Oless__eq [138, 3] (w:1, o:251, a:1, s:1, b:0
% 0.95/1.61 ),
% 0.95/1.61 class_Rings_Ocomm__ring__1 [139, 1] (w:1, o:116, a:1, s:1, b:0),
% 0.95/1.61 c_Groups_Ouminus__class_Ouminus [140, 2] (w:1, o:226, a:1, s:1, b:0)
% 0.95/1.61 ,
% 0.95/1.61 c_Groups_Oone__class_Oone [141, 1] (w:1, o:149, a:1, s:1, b:0),
% 0.95/1.61 class_Rings_Oring__1__no__zero__divisors [142, 1] (w:1, o:158, a:1
% 0.95/1.61 , s:1, b:0),
% 0.95/1.61 class_Rings_Olinordered__semidom [143, 1] (w:1, o:165, a:1, s:1, b:0)
% 0.95/1.61 ,
% 0.95/1.61 class_Groups_Oab__group__add [144, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.95/1.61 class_Rings_Ocomm__ring [145, 1] (w:1, o:117, a:1, s:1, b:0),
% 0.95/1.61 class_Groups_Ogroup__add [146, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.95/1.61 class_Groups_Oone [147, 1] (w:1, o:137, a:1, s:1, b:0),
% 0.95/1.61 class_Groups_Oordered__ab__group__add [148, 1] (w:1, o:138, a:1, s:1
% 0.95/1.61 , b:0),
% 0.95/1.61 class_Rings_Olinordered__idom [149, 1] (w:1, o:166, a:1, s:1, b:0),
% 0.95/1.61 class_Rings_Oring [150, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.95/1.61 class_Rings_Ozero__neq__one [151, 1] (w:1, o:174, a:1, s:1, b:0),
% 0.95/1.61 class_Groups_Omonoid__mult [152, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.95/1.61 class_Groups_Ocomm__monoid__mult [153, 1] (w:1, o:140, a:1, s:1, b:0)
% 0.95/1.61 ,
% 0.95/1.61 class_Groups_Oordered__ab__semigroup__add__imp__le [154, 1] (w:1, o:
% 0.95/1.61 141, a:1, s:1, b:0),
% 0.95/1.61 class_Groups_Oordered__ab__semigroup__add [155, 1] (w:1, o:142, a:1
% 0.95/1.61 , s:1, b:0),
% 0.95/1.61 class_Rings_Olinordered__semiring__1 [159, 1] (w:1, o:167, a:1, s:1
% 0.95/1.61 , b:0),
% 0.95/1.61 class_Rings_Oordered__cancel__semiring [160, 1] (w:1, o:175, a:1, s:1
% 0.95/1.61 , b:0),
% 0.95/1.61 class_Rings_Oordered__ring [161, 1] (w:1, o:176, a:1, s:1, b:0),
% 0.95/1.61 class_Rings_Oordered__semiring [162, 1] (w:1, o:177, a:1, s:1, b:0),
% 0.95/1.61
% 0.95/1.61 class_Rings_Oordered__comm__semiring [163, 1] (w:1, o:178, a:1, s:1
% 0.95/1.61 , b:0),
% 0.95/1.61 class_Rings_Olinordered__ring [164, 1] (w:1, o:164, a:1, s:1, b:0),
% 0.95/1.61 class_Groups_Oordered__comm__monoid__add [165, 1] (w:1, o:143, a:1
% 0.95/1.61 , s:1, b:0),
% 0.95/1.61 class_Orderings_Opreorder [166, 1] (w:1, o:187, a:1, s:1, b:0),
% 0.95/1.61 class_Lattices_Oboolean__algebra [168, 1] (w:1, o:189, a:1, s:1, b:0)
% 0.95/1.61 ,
% 0.95/1.61 class_Fields_Ofield [169, 1] (w:1, o:123, a:1, s:1, b:0),
% 0.95/1.61 c_Polynomial_Opoly__gcd [170, 3] (w:1, o:261, a:1, s:1, b:0),
% 0.95/1.61 class_Orderings_Oord [171, 1] (w:1, o:185, a:1, s:1, b:0),
% 0.95/1.61 tc_fun [172, 2] (w:1, o:238, a:1, s:1, b:0),
% 0.95/1.61 class_Orderings_Olinorder [173, 1] (w:1, o:190, a:1, s:1, b:0),
% 0.95/1.61 class_Orderings_Oorder [174, 1] (w:1, o:186, a:1, s:1, b:0),
% 0.95/1.61 class_Lattices_Oab__semigroup__idem__mult [175, 1] (w:1, o:188, a:1
% 0.95/1.61 , s:1, b:0),
% 0.95/1.61 class_Groups_Ouminus [177, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.95/1.61 c_Rings_Odvd__class_Odvd [178, 3] (w:1, o:262, a:1, s:1, b:0),
% 0.95/1.61 c_Orderings_Oord__class_Oless [179, 3] (w:1, o:252, a:1, s:1, b:0),
% 0.95/1.61 c_Rings_Oinverse__class_Oinverse [180, 2] (w:1, o:239, a:1, s:1, b:0)
% 0.95/1.61 ,
% 0.95/1.61 c_fFalse [181, 0] (w:1, o:88, a:1, s:1, b:0),
% 0.95/1.61 c_HOL_Obool_Obool__size [182, 1] (w:1, o:191, a:1, s:1, b:0),
% 0.95/1.61 class_Rings_Odvd [183, 1] (w:1, o:179, a:1, s:1, b:0),
% 0.95/1.61 class_Rings_Odivision__ring__inverse__zero [184, 1] (w:1, o:180, a:1
% 0.95/1.61 , s:1, b:0),
% 0.95/1.61 class_Rings_Odivision__ring [185, 1] (w:1, o:181, a:1, s:1, b:0),
% 3.56/3.93 class_Groups_Oordered__cancel__ab__semigroup__add [188, 1] (w:1, o:
% 3.56/3.93 145, a:1, s:1, b:0),
% 3.56/3.93 class_Rings_Olinordered__comm__semiring__strict [189, 1] (w:1, o:168
% 3.56/3.93 , a:1, s:1, b:0),
% 3.56/3.93 class_Rings_Olinordered__semiring__strict [190, 1] (w:1, o:169, a:1
% 3.56/3.93 , s:1, b:0),
% 3.56/3.93 class_Rings_Olinordered__semiring [193, 1] (w:1, o:170, a:1, s:1, b:0
% 3.56/3.93 ),
% 3.56/3.93 class_Rings_Olinordered__semiring__1__strict [194, 1] (w:1, o:171, a:
% 3.56/3.93 1, s:1, b:0),
% 3.56/3.93 c_fTrue [195, 0] (w:1, o:94, a:1, s:1, b:0),
% 3.56/3.93 class_Fields_Olinordered__field__inverse__zero [196, 1] (w:1, o:124
% 3.56/3.93 , a:1, s:1, b:0),
% 3.56/3.93 class_Fields_Olinordered__field [197, 1] (w:1, o:125, a:1, s:1, b:0)
% 3.56/3.93 ,
% 3.56/3.93 class_Fields_Ofield__inverse__zero [198, 1] (w:1, o:126, a:1, s:1, b:
% 3.56/3.93 0),
% 3.56/3.93 class_Rings_Osemiring__0 [199, 1] (w:1, o:182, a:1, s:1, b:0),
% 3.56/3.93 c_Power_Opower__class_Opower [200, 1] (w:1, o:192, a:1, s:1, b:0),
% 3.56/3.93 tc_Int_Oint [201, 0] (w:1, o:96, a:1, s:1, b:0),
% 3.56/3.93 class_Power_Opower [202, 1] (w:1, o:193, a:1, s:1, b:0),
% 3.56/3.93 class_Rings_Oring__1 [203, 1] (w:1, o:160, a:1, s:1, b:0),
% 3.56/3.93 c_Power_Opower_Opower [205, 3] (w:1, o:263, a:1, s:1, b:0),
% 3.56/3.93 c_Polynomial_Opdivmod__rel [207, 5] (w:1, o:317, a:1, s:1, b:0),
% 3.56/3.93 c_Polynomial_Opos__poly [208, 2] (w:1, o:240, a:1, s:1, b:0),
% 3.56/3.93 c_Divides_Odiv__class_Omod [225, 3] (w:1, o:264, a:1, s:1, b:0),
% 3.56/3.93 class_Divides_Osemiring__div [226, 1] (w:1, o:195, a:1, s:1, b:0),
% 3.56/3.93 class_Divides_Oring__div [227, 1] (w:1, o:194, a:1, s:1, b:0),
% 3.56/3.93 c_SMT_Oz3mod [234, 2] (w:1, o:241, a:1, s:1, b:0),
% 3.56/3.93 c_Groups_Ominus__class_Ominus [235, 3] (w:1, o:265, a:1, s:1, b:0),
% 3.56/3.93 class_Groups_Ocancel__comm__monoid__add [242, 1] (w:1, o:146, a:1, s:
% 3.56/3.93 1, b:0),
% 3.56/3.93 tc_HOL_Obool [243, 0] (w:1, o:95, a:1, s:1, b:0),
% 3.56/3.93 class_Enum_Oenum [244, 1] (w:1, o:122, a:1, s:1, b:0),
% 3.56/3.93 t_a [246, 0] (w:1, o:108, a:1, s:1, b:0),
% 3.56/3.93 v_a [247, 0] (w:1, o:109, a:1, s:1, b:0),
% 3.56/3.93 v_h [248, 0] (w:1, o:110, a:1, s:1, b:0),
% 3.56/3.93 alpha1 [249, 2] (w:1, o:242, a:1, s:1, b:1),
% 3.56/3.93 alpha2 [250, 2] (w:1, o:246, a:1, s:1, b:1),
% 3.56/3.93 alpha3 [251, 3] (w:1, o:272, a:1, s:1, b:1),
% 3.56/3.93 alpha4 [252, 3] (w:1, o:282, a:1, s:1, b:1),
% 3.56/3.93 alpha5 [253, 4] (w:1, o:308, a:1, s:1, b:1),
% 3.56/3.93 alpha6 [254, 4] (w:1, o:309, a:1, s:1, b:1),
% 3.56/3.93 alpha7 [255, 2] (w:1, o:247, a:1, s:1, b:1),
% 3.56/3.93 alpha8 [256, 3] (w:1, o:283, a:1, s:1, b:1),
% 3.56/3.93 alpha9 [257, 2] (w:1, o:248, a:1, s:1, b:1),
% 3.56/3.93 alpha10 [258, 2] (w:1, o:243, a:1, s:1, b:1),
% 3.56/3.93 alpha11 [259, 3] (w:1, o:284, a:1, s:1, b:1),
% 3.56/3.93 alpha12 [260, 3] (w:1, o:285, a:1, s:1, b:1),
% 3.56/3.93 alpha13 [261, 3] (w:1, o:286, a:1, s:1, b:1),
% 3.56/3.93 alpha14 [262, 3] (w:1, o:287, a:1, s:1, b:1),
% 3.56/3.93 alpha15 [263, 2] (w:1, o:244, a:1, s:1, b:1),
% 3.56/3.93 alpha16 [264, 2] (w:1, o:245, a:1, s:1, b:1),
% 3.56/3.93 alpha17 [265, 3] (w:1, o:288, a:1, s:1, b:1),
% 3.56/3.93 alpha18 [266, 3] (w:1, o:289, a:1, s:1, b:1),
% 3.56/3.93 alpha19 [267, 4] (w:1, o:310, a:1, s:1, b:1),
% 3.56/3.93 alpha20 [268, 4] (w:1, o:311, a:1, s:1, b:1),
% 3.56/3.93 alpha21 [269, 4] (w:1, o:312, a:1, s:1, b:1),
% 3.56/3.93 alpha22 [270, 3] (w:1, o:266, a:1, s:1, b:1),
% 3.56/3.93 alpha23 [271, 3] (w:1, o:267, a:1, s:1, b:1),
% 3.56/3.93 alpha24 [272, 3] (w:1, o:268, a:1, s:1, b:1),
% 3.56/3.93 alpha25 [273, 4] (w:1, o:313, a:1, s:1, b:1),
% 3.56/3.93 alpha26 [274, 3] (w:1, o:269, a:1, s:1, b:1),
% 3.56/3.93 alpha27 [275, 3] (w:1, o:270, a:1, s:1, b:1),
% 3.56/3.93 alpha28 [276, 3] (w:1, o:271, a:1, s:1, b:1),
% 3.56/3.93 alpha29 [277, 4] (w:1, o:314, a:1, s:1, b:1),
% 3.56/3.93 alpha30 [278, 3] (w:1, o:273, a:1, s:1, b:1),
% 3.56/3.93 alpha31 [279, 3] (w:1, o:274, a:1, s:1, b:1),
% 3.56/3.93 alpha32 [280, 3] (w:1, o:275, a:1, s:1, b:1),
% 3.56/3.93 alpha33 [281, 3] (w:1, o:276, a:1, s:1, b:1),
% 3.56/3.93 alpha34 [282, 3] (w:1, o:277, a:1, s:1, b:1),
% 3.56/3.93 alpha35 [283, 3] (w:1, o:278, a:1, s:1, b:1),
% 3.56/3.93 alpha36 [284, 3] (w:1, o:279, a:1, s:1, b:1),
% 3.56/3.93 alpha37 [285, 3] (w:1, o:280, a:1, s:1, b:1),
% 3.56/3.93 alpha38 [286, 3] (w:1, o:281, a:1, s:1, b:1),
% 3.56/3.93 alpha39 [287, 2] (w:1, o:249, a:1, s:1, b:1),
% 30.18/30.59 alpha40 [288, 3] (w:1, o:290, a:1, s:1, b:1),
% 30.18/30.59 alpha41 [289, 4] (w:1, o:305, a:1, s:1, b:1),
% 30.18/30.59 alpha42 [290, 4] (w:1, o:306, a:1, s:1, b:1),
% 30.18/30.59 alpha43 [291, 4] (w:1, o:307, a:1, s:1, b:1),
% 30.18/30.59 skol1 [292, 2] (w:1, o:227, a:1, s:1, b:1),
% 30.18/30.59 skol2 [293, 2] (w:1, o:232, a:1, s:1, b:1),
% 30.18/30.59 skol3 [294, 3] (w:1, o:297, a:1, s:1, b:1),
% 30.18/30.59 skol4 [295, 2] (w:1, o:233, a:1, s:1, b:1),
% 30.18/30.59 skol5 [296, 2] (w:1, o:234, a:1, s:1, b:1),
% 30.18/30.59 skol6 [297, 3] (w:1, o:298, a:1, s:1, b:1),
% 30.18/30.59 skol7 [298, 1] (w:1, o:119, a:1, s:1, b:1),
% 30.18/30.59 skol8 [299, 2] (w:1, o:235, a:1, s:1, b:1),
% 30.18/30.59 skol9 [300, 2] (w:1, o:236, a:1, s:1, b:1),
% 30.18/30.59 skol10 [301, 3] (w:1, o:299, a:1, s:1, b:1),
% 30.18/30.59 skol11 [302, 4] (w:1, o:315, a:1, s:1, b:1),
% 30.18/30.59 skol12 [303, 3] (w:1, o:300, a:1, s:1, b:1),
% 30.18/30.59 skol13 [304, 2] (w:1, o:228, a:1, s:1, b:1),
% 30.18/30.59 skol14 [305, 2] (w:1, o:229, a:1, s:1, b:1),
% 30.18/30.59 skol15 [306, 3] (w:1, o:301, a:1, s:1, b:1),
% 30.18/30.59 skol16 [307, 3] (w:1, o:302, a:1, s:1, b:1),
% 30.18/30.59 skol17 [308, 2] (w:1, o:230, a:1, s:1, b:1),
% 30.18/30.59 skol18 [309, 2] (w:1, o:231, a:1, s:1, b:1),
% 30.18/30.59 skol19 [310, 3] (w:1, o:303, a:1, s:1, b:1),
% 30.18/30.59 skol20 [311, 3] (w:1, o:291, a:1, s:1, b:1),
% 30.18/30.59 skol21 [312, 3] (w:1, o:292, a:1, s:1, b:1),
% 30.18/30.59 skol22 [313, 3] (w:1, o:293, a:1, s:1, b:1),
% 30.18/30.59 skol23 [314, 3] (w:1, o:294, a:1, s:1, b:1),
% 30.18/30.59 skol24 [315, 3] (w:1, o:295, a:1, s:1, b:1),
% 30.18/30.59 skol25 [316, 2] (w:1, o:237, a:1, s:1, b:1),
% 30.18/30.59 skol26 [317, 3] (w:1, o:296, a:1, s:1, b:1).
% 30.18/30.59
% 30.18/30.59
% 30.18/30.59 Starting Search:
% 30.18/30.59
% 30.18/30.59 *** allocated 113905 integers for clauses
% 30.18/30.59 *** allocated 170857 integers for clauses
% 30.18/30.59 Resimplifying inuse:
% 30.18/30.59 Done
% 30.18/30.59
% 30.18/30.59
% 30.18/30.59 Intermediate Status:
% 30.18/30.59 Generated: 3334
% 30.18/30.59 Kept: 2034
% 30.18/30.59 Inuse: 40
% 30.18/30.59 Deleted: 1
% 30.18/30.59 Deletedinuse: 0
% 30.18/30.59
% 30.18/30.59 *** allocated 256285 integers for clauses
% 30.18/30.59 *** allocated 170857 integers for termspace/termends
% 30.18/30.59 Resimplifying inuse:
% 30.18/30.59 Done
% 30.18/30.59
% 30.18/30.59 Resimplifying inuse:
% 30.18/30.59 Done
% 30.18/30.59
% 30.18/30.59
% 30.18/30.59 Intermediate Status:
% 30.18/30.59 Generated: 8400
% 30.18/30.59 Kept: 4034
% 30.18/30.59 Inuse: 143
% 30.18/30.59 Deleted: 8
% 30.18/30.59 Deletedinuse: 0
% 30.18/30.59
% 30.18/30.59 *** allocated 384427 integers for clauses
% 30.18/30.59 Resimplifying inuse:
% 30.18/30.59 Done
% 30.18/30.59
% 30.18/30.59 *** allocated 256285 integers for termspace/termends
% 30.18/30.59
% 30.18/30.59 Intermediate Status:
% 30.18/30.59 Generated: 13212
% 30.18/30.59 Kept: 6260
% 30.18/30.59 Inuse: 209
% 30.18/30.59 Deleted: 12
% 30.18/30.59 Deletedinuse: 0
% 30.18/30.59
% 30.18/30.59 Resimplifying inuse:
% 30.18/30.59 Done
% 30.18/30.59
% 30.18/30.59 *** allocated 576640 integers for clauses
% 30.18/30.59 Resimplifying inuse:
% 30.18/30.59 Done
% 30.18/30.59
% 30.18/30.59 *** allocated 384427 integers for termspace/termends
% 30.18/30.59
% 30.18/30.59 Intermediate Status:
% 30.18/30.59 Generated: 21375
% 30.18/30.59 Kept: 8625
% 30.18/30.59 Inuse: 244
% 30.18/30.59 Deleted: 13
% 30.18/30.59 Deletedinuse: 1
% 30.18/30.59
% 30.18/30.59 Resimplifying inuse:
% 30.18/30.59 Done
% 30.18/30.59
% 30.18/30.59 Resimplifying inuse:
% 30.18/30.59 Done
% 30.18/30.59
% 30.18/30.59 *** allocated 864960 integers for clauses
% 30.18/30.59
% 30.18/30.59 Intermediate Status:
% 30.18/30.59 Generated: 28156
% 30.18/30.59 Kept: 11041
% 30.18/30.59 Inuse: 294
% 30.18/30.59 Deleted: 13
% 30.18/30.59 Deletedinuse: 1
% 30.18/30.59
% 30.18/30.59 Resimplifying inuse:
% 30.18/30.59 Done
% 30.18/30.59
% 30.18/30.59 Resimplifying inuse:
% 30.18/30.59 Done
% 30.18/30.59
% 30.18/30.59 *** allocated 576640 integers for termspace/termends
% 30.18/30.59
% 30.18/30.59 Intermediate Status:
% 30.18/30.59 Generated: 35848
% 30.18/30.59 Kept: 13521
% 30.18/30.59 Inuse: 329
% 30.18/30.59 Deleted: 13
% 30.18/30.59 Deletedinuse: 1
% 30.18/30.59
% 30.18/30.59 Resimplifying inuse:
% 30.18/30.59 Done
% 30.18/30.59
% 30.18/30.59 Resimplifying inuse:
% 30.18/30.59 Done
% 30.18/30.59
% 30.18/30.59
% 30.18/30.59 Intermediate Status:
% 30.18/30.59 Generated: 42744
% 30.18/30.59 Kept: 15527
% 30.18/30.59 Inuse: 353
% 30.18/30.59 Deleted: 13
% 30.18/30.59 Deletedinuse: 1
% 30.18/30.59
% 30.18/30.59 Resimplifying inuse:
% 30.18/30.59 Done
% 30.18/30.59
% 30.18/30.59 *** allocated 1297440 integers for clauses
% 30.18/30.59 Resimplifying inuse:
% 30.18/30.59 Done
% 30.18/30.59
% 30.18/30.59
% 30.18/30.59 Intermediate Status:
% 30.18/30.59 Generated: 49619
% 30.18/30.59 Kept: 18282
% 30.18/30.59 Inuse: 404
% 30.18/30.59 Deleted: 13
% 30.18/30.59 Deletedinuse: 1
% 30.18/30.59
% 30.18/30.59 Resimplifying inuse:
% 30.18/30.59 Done
% 30.18/30.59
% 30.18/30.59 Resimplifying inuse:
% 30.18/30.59 Done
% 30.18/30.59
% 30.18/30.59
% 30.18/30.59 Intermediate Status:
% 30.18/30.59 Generated: 56162
% 30.18/30.59 Kept: 20404
% 30.18/30.59 Inuse: 439
% 30.18/30.59 Deleted: 13
% 30.18/30.59 Deletedinuse: 1
% 30.18/30.59
% 30.18/30.59 Resimplifying inuse:
% 30.18/30.59 Done
% 30.18/30.59
% 30.18/30.59 Resimplifying clauses:
% 30.18/30.59 Done
% 30.18/30.59
% 30.18/30.59 Resimplifying inuse:
% 30.18/30.59 Done
% 30.18/30.59
% 30.18/30.59 *** allocated 864960 integers for termspace/termends
% 30.18/30.59
% 30.18/30.59 Intermediate Status:
% 30.18/30.59 Generated: 60540
% 30.18/30.59 Kept: 22416
% 30.18/30.59 Inuse: 464
% 30.18/30.59 Deleted: 175
% 30.18/30.59 Deletedinuse: 1
% 30.18/30.59
% 30.18/30.59 Resimplifying inuse:
% 30.18/30.59 Done
% 30.18/30.59
% 30.18/30.59
% 30.18/30.59 Intermediate Status:
% 30.18/30.59 Generated: 77164
% 30.18/30.59 Kept: 25339
% 30.18/30.59 Inuse: 499
% 30.18/30.59 Deleted: 175
% 30.18/30.59 Deletedinuse: 1
% 30.18/30.59
% 30.18/30.59 Resimplifying inuse:
% 30.18/30.59 Done
% 30.18/30.59
% 30.18/30.59 *** allocated 1946160 integers for clauses
% 30.18/30.59 Resimplifying inuse:
% 30.18/30.59 Done
% 30.18/30.59
% 30.18/30.59
% 30.18/30.59 Intermediate Status:
% 30.18/30.59 Generated: 105806
% 74.94/75.39 Kept: 28703
% 74.94/75.39 Inuse: 549
% 74.94/75.39 Deleted: 175
% 74.94/75.39 Deletedinuse: 1
% 74.94/75.39
% 74.94/75.39 Resimplifying inuse:
% 74.94/75.39 Done
% 74.94/75.39
% 74.94/75.39 *** allocated 1297440 integers for termspace/termends
% 74.94/75.39 Resimplifying inuse:
% 74.94/75.39 Done
% 74.94/75.39
% 74.94/75.39
% 74.94/75.39 Intermediate Status:
% 74.94/75.39 Generated: 118889
% 74.94/75.39 Kept: 31025
% 74.94/75.39 Inuse: 578
% 74.94/75.39 Deleted: 175
% 74.94/75.39 Deletedinuse: 1
% 74.94/75.39
% 74.94/75.39 Resimplifying inuse:
% 74.94/75.39 Done
% 74.94/75.39
% 74.94/75.39 Resimplifying inuse:
% 74.94/75.39 Done
% 74.94/75.39
% 74.94/75.39
% 74.94/75.39 Intermediate Status:
% 74.94/75.39 Generated: 124375
% 74.94/75.39 Kept: 34057
% 74.94/75.39 Inuse: 589
% 74.94/75.39 Deleted: 175
% 74.94/75.39 Deletedinuse: 1
% 74.94/75.39
% 74.94/75.39 Resimplifying inuse:
% 74.94/75.39 Done
% 74.94/75.39
% 74.94/75.39 Resimplifying inuse:
% 74.94/75.39 Done
% 74.94/75.39
% 74.94/75.39
% 74.94/75.39 Intermediate Status:
% 74.94/75.39 Generated: 139051
% 74.94/75.39 Kept: 37283
% 74.94/75.39 Inuse: 613
% 74.94/75.39 Deleted: 176
% 74.94/75.39 Deletedinuse: 1
% 74.94/75.39
% 74.94/75.39 Resimplifying inuse:
% 74.94/75.39 Done
% 74.94/75.39
% 74.94/75.39 Resimplifying inuse:
% 74.94/75.39 Done
% 74.94/75.39
% 74.94/75.39
% 74.94/75.39 Intermediate Status:
% 74.94/75.39 Generated: 172483
% 74.94/75.39 Kept: 40516
% 74.94/75.39 Inuse: 637
% 74.94/75.39 Deleted: 177
% 74.94/75.39 Deletedinuse: 1
% 74.94/75.39
% 74.94/75.39 Resimplifying inuse:
% 74.94/75.39 Done
% 74.94/75.39
% 74.94/75.39 Resimplifying clauses:
% 74.94/75.39 Done
% 74.94/75.39
% 74.94/75.39 *** allocated 2919240 integers for clauses
% 74.94/75.39 Resimplifying inuse:
% 74.94/75.39 Done
% 74.94/75.39
% 74.94/75.39
% 74.94/75.39 Intermediate Status:
% 74.94/75.39 Generated: 206247
% 74.94/75.39 Kept: 44072
% 74.94/75.39 Inuse: 672
% 75.02/75.40 Deleted: 476
% 75.02/75.40 Deletedinuse: 1
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40 *** allocated 1946160 integers for termspace/termends
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40
% 75.02/75.40 Intermediate Status:
% 75.02/75.40 Generated: 219633
% 75.02/75.40 Kept: 46854
% 75.02/75.40 Inuse: 702
% 75.02/75.40 Deleted: 476
% 75.02/75.40 Deletedinuse: 1
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40
% 75.02/75.40 Intermediate Status:
% 75.02/75.40 Generated: 230331
% 75.02/75.40 Kept: 50279
% 75.02/75.40 Inuse: 717
% 75.02/75.40 Deleted: 476
% 75.02/75.40 Deletedinuse: 1
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40
% 75.02/75.40 Intermediate Status:
% 75.02/75.40 Generated: 236724
% 75.02/75.40 Kept: 53689
% 75.02/75.40 Inuse: 727
% 75.02/75.40 Deleted: 476
% 75.02/75.40 Deletedinuse: 1
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40
% 75.02/75.40 Intermediate Status:
% 75.02/75.40 Generated: 241030
% 75.02/75.40 Kept: 55762
% 75.02/75.40 Inuse: 737
% 75.02/75.40 Deleted: 476
% 75.02/75.40 Deletedinuse: 1
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40
% 75.02/75.40 Intermediate Status:
% 75.02/75.40 Generated: 249918
% 75.02/75.40 Kept: 57972
% 75.02/75.40 Inuse: 757
% 75.02/75.40 Deleted: 476
% 75.02/75.40 Deletedinuse: 1
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40
% 75.02/75.40 Intermediate Status:
% 75.02/75.40 Generated: 258275
% 75.02/75.40 Kept: 60062
% 75.02/75.40 Inuse: 782
% 75.02/75.40 Deleted: 476
% 75.02/75.40 Deletedinuse: 1
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40 Resimplifying clauses:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40
% 75.02/75.40 Intermediate Status:
% 75.02/75.40 Generated: 267731
% 75.02/75.40 Kept: 62088
% 75.02/75.40 Inuse: 812
% 75.02/75.40 Deleted: 521
% 75.02/75.40 Deletedinuse: 1
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40 *** allocated 4378860 integers for clauses
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40
% 75.02/75.40 Intermediate Status:
% 75.02/75.40 Generated: 277905
% 75.02/75.40 Kept: 64096
% 75.02/75.40 Inuse: 846
% 75.02/75.40 Deleted: 521
% 75.02/75.40 Deletedinuse: 1
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40
% 75.02/75.40 Intermediate Status:
% 75.02/75.40 Generated: 290726
% 75.02/75.40 Kept: 67029
% 75.02/75.40 Inuse: 862
% 75.02/75.40 Deleted: 521
% 75.02/75.40 Deletedinuse: 1
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40
% 75.02/75.40 Intermediate Status:
% 75.02/75.40 Generated: 301067
% 75.02/75.40 Kept: 69428
% 75.02/75.40 Inuse: 872
% 75.02/75.40 Deleted: 521
% 75.02/75.40 Deletedinuse: 1
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40 *** allocated 2919240 integers for termspace/termends
% 75.02/75.40
% 75.02/75.40 Intermediate Status:
% 75.02/75.40 Generated: 320211
% 75.02/75.40 Kept: 71725
% 75.02/75.40 Inuse: 882
% 75.02/75.40 Deleted: 521
% 75.02/75.40 Deletedinuse: 1
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40
% 75.02/75.40 Intermediate Status:
% 75.02/75.40 Generated: 338030
% 75.02/75.40 Kept: 73750
% 75.02/75.40 Inuse: 889
% 75.02/75.40 Deleted: 521
% 75.02/75.40 Deletedinuse: 1
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40
% 75.02/75.40 Intermediate Status:
% 75.02/75.40 Generated: 351442
% 75.02/75.40 Kept: 76750
% 75.02/75.40 Inuse: 917
% 75.02/75.40 Deleted: 521
% 75.02/75.40 Deletedinuse: 1
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40
% 75.02/75.40 Intermediate Status:
% 75.02/75.40 Generated: 369371
% 75.02/75.40 Kept: 80398
% 75.02/75.40 Inuse: 932
% 75.02/75.40 Deleted: 521
% 75.02/75.40 Deletedinuse: 1
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40 Resimplifying clauses:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40
% 75.02/75.40 Intermediate Status:
% 75.02/75.40 Generated: 379556
% 75.02/75.40 Kept: 82566
% 75.02/75.40 Inuse: 962
% 75.02/75.40 Deleted: 558
% 75.02/75.40 Deletedinuse: 1
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40
% 75.02/75.40 Intermediate Status:
% 75.02/75.40 Generated: 397556
% 75.02/75.40 Kept: 86567
% 75.02/75.40 Inuse: 1002
% 75.02/75.40 Deleted: 558
% 75.02/75.40 Deletedinuse: 1
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40
% 75.02/75.40 Intermediate Status:
% 75.02/75.40 Generated: 405960
% 75.02/75.40 Kept: 89140
% 75.02/75.40 Inuse: 1012
% 75.02/75.40 Deleted: 558
% 75.02/75.40 Deletedinuse: 1
% 75.02/75.40
% 75.02/75.40 Resimplifying inuse:
% 75.02/75.40 Done
% 75.02/75.40
% 75.02/75.40
% 75.02/75.40 Intermediate Status:
% 75.02/75.40 Generated: 417780
% 75.02/75.40 Kept: 92156
% 75.02/75.40 Inuse: 1027
% 158.13/158.51 Deleted: 558
% 158.13/158.51 Deletedinuse: 1
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 426154
% 158.13/158.51 Kept: 94177
% 158.13/158.51 Inuse: 1059
% 158.13/158.51 Deleted: 558
% 158.13/158.51 Deletedinuse: 1
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 433991
% 158.13/158.51 Kept: 96245
% 158.13/158.51 Inuse: 1092
% 158.13/158.51 Deleted: 558
% 158.13/158.51 Deletedinuse: 1
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51 *** allocated 6568290 integers for clauses
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 443722
% 158.13/158.51 Kept: 99952
% 158.13/158.51 Inuse: 1107
% 158.13/158.51 Deleted: 558
% 158.13/158.51 Deletedinuse: 1
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 451054
% 158.13/158.51 Kept: 103200
% 158.13/158.51 Inuse: 1117
% 158.13/158.51 Deleted: 558
% 158.13/158.51 Deletedinuse: 1
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51 Resimplifying clauses:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51 *** allocated 4378860 integers for termspace/termends
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 479687
% 158.13/158.51 Kept: 107161
% 158.13/158.51 Inuse: 1132
% 158.13/158.51 Deleted: 1119
% 158.13/158.51 Deletedinuse: 1
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 490026
% 158.13/158.51 Kept: 109377
% 158.13/158.51 Inuse: 1152
% 158.13/158.51 Deleted: 1119
% 158.13/158.51 Deletedinuse: 1
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 499310
% 158.13/158.51 Kept: 111446
% 158.13/158.51 Inuse: 1185
% 158.13/158.51 Deleted: 1121
% 158.13/158.51 Deletedinuse: 1
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 508376
% 158.13/158.51 Kept: 113464
% 158.13/158.51 Inuse: 1212
% 158.13/158.51 Deleted: 1121
% 158.13/158.51 Deletedinuse: 1
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 515659
% 158.13/158.51 Kept: 115468
% 158.13/158.51 Inuse: 1239
% 158.13/158.51 Deleted: 1121
% 158.13/158.51 Deletedinuse: 1
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 522566
% 158.13/158.51 Kept: 118310
% 158.13/158.51 Inuse: 1245
% 158.13/158.51 Deleted: 1121
% 158.13/158.51 Deletedinuse: 1
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 529491
% 158.13/158.51 Kept: 120414
% 158.13/158.51 Inuse: 1255
% 158.13/158.51 Deleted: 1121
% 158.13/158.51 Deletedinuse: 1
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 538336
% 158.13/158.51 Kept: 122425
% 158.13/158.51 Inuse: 1287
% 158.13/158.51 Deleted: 1121
% 158.13/158.51 Deletedinuse: 1
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51 Resimplifying clauses:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 547421
% 158.13/158.51 Kept: 124433
% 158.13/158.51 Inuse: 1316
% 158.13/158.51 Deleted: 1629
% 158.13/158.51 Deletedinuse: 1
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 557209
% 158.13/158.51 Kept: 126549
% 158.13/158.51 Inuse: 1350
% 158.13/158.51 Deleted: 1629
% 158.13/158.51 Deletedinuse: 1
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 565591
% 158.13/158.51 Kept: 128576
% 158.13/158.51 Inuse: 1369
% 158.13/158.51 Deleted: 1629
% 158.13/158.51 Deletedinuse: 1
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 576059
% 158.13/158.51 Kept: 131664
% 158.13/158.51 Inuse: 1385
% 158.13/158.51 Deleted: 1629
% 158.13/158.51 Deletedinuse: 1
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 582729
% 158.13/158.51 Kept: 134129
% 158.13/158.51 Inuse: 1390
% 158.13/158.51 Deleted: 1629
% 158.13/158.51 Deletedinuse: 1
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 597582
% 158.13/158.51 Kept: 136686
% 158.13/158.51 Inuse: 1415
% 158.13/158.51 Deleted: 1629
% 158.13/158.51 Deletedinuse: 1
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 608883
% 158.13/158.51 Kept: 138877
% 158.13/158.51 Inuse: 1425
% 158.13/158.51 Deleted: 1629
% 158.13/158.51 Deletedinuse: 1
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 615813
% 158.13/158.51 Kept: 140913
% 158.13/158.51 Inuse: 1433
% 158.13/158.51 Deleted: 1629
% 158.13/158.51 Deletedinuse: 1
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 631645
% 158.13/158.51 Kept: 143396
% 158.13/158.51 Inuse: 1447
% 158.13/158.51 Deleted: 1632
% 158.13/158.51 Deletedinuse: 1
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51 Resimplifying clauses:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 640364
% 158.13/158.51 Kept: 145427
% 158.13/158.51 Inuse: 1468
% 158.13/158.51 Deleted: 1968
% 158.13/158.51 Deletedinuse: 2
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 656089
% 158.13/158.51 Kept: 147678
% 158.13/158.51 Inuse: 1482
% 158.13/158.51 Deleted: 1968
% 158.13/158.51 Deletedinuse: 2
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate Status:
% 158.13/158.51 Generated: 665047
% 158.13/158.51 Kept: 149793
% 158.13/158.51 Inuse: 1497
% 158.13/158.51 Deleted: 1968
% 158.13/158.51 Deletedinuse: 2
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51 Resimplifying inuse:
% 158.13/158.51 Done
% 158.13/158.51
% 158.13/158.51
% 158.13/158.51 Intermediate StaCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------