TSTP Solution File: SWW247+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW247+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n022.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 23:21:32 EDT 2022
% Result : Timeout 300.03s 300.43s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWW247+1 : TPTP v8.1.0. Released v5.2.0.
% 0.10/0.12 % Command : bliksem %s
% 0.11/0.33 % Computer : n022.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % DateTime : Mon Jun 6 04:57:05 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.99/1.62 *** allocated 10000 integers for termspace/termends
% 0.99/1.62 *** allocated 10000 integers for clauses
% 0.99/1.62 *** allocated 10000 integers for justifications
% 0.99/1.62 *** allocated 15000 integers for termspace/termends
% 0.99/1.62 *** allocated 22500 integers for termspace/termends
% 0.99/1.62 *** allocated 33750 integers for termspace/termends
% 0.99/1.62 Bliksem 1.12
% 0.99/1.62
% 0.99/1.62
% 0.99/1.62 Automatic Strategy Selection
% 0.99/1.62
% 0.99/1.62 *** allocated 50625 integers for termspace/termends
% 0.99/1.62 *** allocated 75937 integers for termspace/termends
% 0.99/1.62 *** allocated 113905 integers for termspace/termends
% 0.99/1.62 *** allocated 170857 integers for termspace/termends
% 0.99/1.62
% 0.99/1.62 Clauses:
% 0.99/1.62
% 0.99/1.62 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.99/1.62 { ! class_Rings_Oidom( t_a ), !
% 0.99/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( t_a, t_a,
% 0.99/1.62 c_Polynomial_Opoly( t_a, v_p ) ) }.
% 0.99/1.62 { ! class_Rings_Oidom( t_a ), X = c_Groups_Ozero__class_Ozero( t_a ), hAPP
% 0.99/1.62 ( c_Polynomial_Opoly( t_a, v_cs____ ), X ) = c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( t_a ) }.
% 0.99/1.62 { ! class_Rings_Oidom( t_a ), !
% 0.99/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( t_a, t_a,
% 0.99/1.62 c_Polynomial_Opoly( t_a, hAPP( hAPP( c_Polynomial_OpCons( t_a ), v_c____
% 0.99/1.62 ), v_cs____ ) ) ) }.
% 0.99/1.62 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.99/1.62 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.99/1.62 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.99/1.62 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( c_Polynomial_OpCons( X ), U ), T
% 0.99/1.62 ) = hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y ), U = Z }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( c_Polynomial_OpCons( X ), U ), T
% 0.99/1.62 ) = hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y ), T = Y }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, hAPP( hAPP(
% 0.99/1.62 c_Polynomial_OpCons( X ), U ), T ) = hAPP( hAPP( c_Polynomial_OpCons( X )
% 0.99/1.62 , Z ), Y ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.99/1.62 hAPP( hAPP( c_Polynomial_OpCons( X ), T ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Polynomial_OpCons( X ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ),
% 0.99/1.62 c_Polynomial_Osynthetic__div( X, Z, Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.62 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.99/1.62 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.99/1.62 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 0.99/1.62 X, T ) = hAPP( X, U ) }.
% 0.99/1.62 { ! hAPP( X, skol2( X ) ) = hAPP( X, skol28( X ) ),
% 0.99/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), Y = hAPP( hAPP( c_Polynomial_OpCons( X ),
% 0.99/1.62 skol3( X, Y ) ), skol29( X, Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.99/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, hAPP( hAPP(
% 0.99/1.62 c_Polynomial_OpCons( X ), Z ), c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) ), Y ) = hAPP( hAPP( c_Polynomial_OpCons( X )
% 0.99/1.62 , Z ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.99/1.62 ( hAPP( c_Polynomial_OpCons( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.99/1.62 , Y ) ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 0.99/1.62 ) = hAPP( c_Polynomial_Opoly( X, T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.99/1.62 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.99/1.62 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Z ), hAPP( hAPP
% 0.99/1.62 ( c_Polynomial_Osmult( X ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.99/1.62 ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP( c_Polynomial_Opoly( X
% 0.99/1.62 , Z ), Y ) ), c_Polynomial_Osynthetic__div( X, Z, Y ) ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), hAPP( hAPP( c_Polynomial_OpCons( X ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 0.99/1.62 ), c_Groups_Ozero__class_Ozero( X ) ), Y ) = c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.99/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) = Y }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 0.99/1.62 ), Y ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Y ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), hAPP(
% 0.99/1.62 hAPP( c_Polynomial_Osmult( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Polynomial_Osmult( X ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 0.99/1.62 ), T ), hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Polynomial_Osmult( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.99/1.62 , T ), Z ) ), Y ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), hAPP(
% 0.99/1.62 hAPP( c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_Osmult( X ), Z ), T ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 0.99/1.62 ), c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 0.99/1.62 .
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 0.99/1.62 ), T ), hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Polynomial_OpCons( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.99/1.62 , T ), Z ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 0.99/1.62 ), T ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X
% 0.99/1.62 ) ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z
% 0.99/1.62 ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), !
% 0.99/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Polynomial_Opoly( X ) ),
% 0.99/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y
% 0.99/1.62 ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y
% 0.99/1.62 ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_OpCons( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y
% 0.99/1.62 ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.99/1.62 hAPP( c_Polynomial_Osmult( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y
% 0.99/1.62 ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.99/1.62 ( hAPP( c_Polynomial_Osmult( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.99/1.62 , Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_Osmult( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Polynomial_Osmult( X ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X, hAPP(
% 0.99/1.62 hAPP( c_Polynomial_OpCons( X ), T ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_OpCons( X ), T ), c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( tc_Polynomial_Opoly( X ) ), Y ), c_Polynomial_Opcompose( X, Z, Y ) ) )
% 0.99/1.62 }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_OpCons( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_Osmult( X ), T ), Y ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 0.99/1.62 ), c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 0.99/1.62 .
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.99/1.62 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T ), Z )
% 0.99/1.62 ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP(
% 0.99/1.62 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.99/1.62 ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.99/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.99/1.62 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.99/1.62 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.99/1.62 ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 0.99/1.62 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP
% 0.99/1.62 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP(
% 0.99/1.62 hAPP( c_Polynomial_Osmult( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_Osmult( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T ), Z ) ), Y )
% 0.99/1.62 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 0.99/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T
% 0.99/1.62 ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 0.99/1.62 ( X ) ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_OpCons( X ), U ), T ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 0.99/1.62 ), Z ), Y ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! hAPP( hAPP( c_Polynomial_Osmult
% 0.99/1.62 ( X ), T ), Y ) = hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y ), Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_Osmult( X ), T ), Y ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 0.99/1.62 ), Z ), Y ) ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) )
% 0.99/1.62 , Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.99/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, hAPP( hAPP(
% 0.99/1.62 c_Polynomial_OpCons( X ), T ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_Osmult( X ), Y ),
% 0.99/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ),
% 0.99/1.62 hAPP( hAPP( c_Polynomial_OpCons( X ), T ),
% 0.99/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 0.99/1.62 .
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), U ), hAPP( hAPP
% 0.99/1.62 ( c_Polynomial_Osmult( X ), T ), Z ) ) = hAPP( hAPP( c_Polynomial_OpCons
% 0.99/1.62 ( X ), Y ), Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), U ), hAPP( hAPP
% 0.99/1.62 ( c_Polynomial_Osmult( X ), T ), Z ) ) = hAPP( hAPP( c_Polynomial_OpCons
% 0.99/1.62 ( X ), Y ), Z ), Z = c_Polynomial_Osynthetic__div( X, U, T ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.99/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.99/1.62 c_Polynomial_Opoly__rec( tc_Polynomial_Opoly( X ), X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.99/1.62 c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 0.99/1.62 tc_fun( tc_Polynomial_Opoly( X ), tc_fun( tc_Polynomial_Opoly( X ),
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) ), X ), c_COMBK( tc_fun( tc_Polynomial_Opoly(
% 0.99/1.62 X ), tc_Polynomial_Opoly( X ) ), tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP
% 0.99/1.62 ( c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 0.99/1.62 tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), X ), hAPP(
% 0.99/1.62 c_COMBS( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 0.99/1.62 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_COMBB( tc_Polynomial_Opoly( X )
% 0.99/1.62 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 0.99/1.62 tc_Polynomial_Opoly( X ) ), c_Groups_Oplus__class_Oplus(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) ), hAPP( c_Polynomial_Osmult( X ), Y ) ) ) ),
% 0.99/1.62 c_Polynomial_OpCons( X ) ) ), Z ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.99/1.62 .
% 0.99/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.99/1.62 .
% 0.99/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.62 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.62 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, ! hAPP( hAPP
% 0.99/1.62 ( c_Groups_Oplus__class_Oplus( X ), W ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), U ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) =
% 0.99/1.62 c_Polynomial_Opoly__rec( tc_Polynomial_Opoly( X ), X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.99/1.62 c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 0.99/1.62 tc_fun( tc_Polynomial_Opoly( X ), tc_fun( tc_Polynomial_Opoly( X ),
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) ), X ), c_COMBK( tc_fun( tc_Polynomial_Opoly(
% 0.99/1.62 X ), tc_Polynomial_Opoly( X ) ), tc_Polynomial_Opoly( X ) ) ), hAPP(
% 0.99/1.62 c_COMBC( X, tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) )
% 0.99/1.62 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), hAPP(
% 0.99/1.62 hAPP( c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X )
% 0.99/1.62 ), tc_fun( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) )
% 0.99/1.62 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ) ), X ),
% 0.99/1.62 c_COMBB( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP( c_COMBB( tc_Polynomial_Opoly( X
% 0.99/1.62 ), tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), X ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ) ), hAPP( c_COMBC
% 0.99/1.62 ( X, tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 0.99/1.62 c_Polynomial_Osmult( X ) ), Y ) ) ) ), hAPP( c_Polynomial_OpCons( X ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ) ), Z ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X, Z, Y )
% 0.99/1.62 = c_Polynomial_Opoly__rec( tc_Polynomial_Opoly( X ), X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.99/1.62 c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 0.99/1.62 tc_fun( tc_Polynomial_Opoly( X ), tc_fun( tc_Polynomial_Opoly( X ),
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) ), X ), c_COMBK( tc_fun( tc_Polynomial_Opoly(
% 0.99/1.62 X ), tc_Polynomial_Opoly( X ) ), tc_Polynomial_Opoly( X ) ) ), hAPP(
% 0.99/1.62 c_COMBC( X, tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) )
% 0.99/1.62 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), hAPP(
% 0.99/1.62 hAPP( c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X )
% 0.99/1.62 ), tc_fun( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) )
% 0.99/1.62 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ) ), X ),
% 0.99/1.62 c_COMBB( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP( c_COMBB( tc_Polynomial_Opoly( X
% 0.99/1.62 ), tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), X ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ) ), hAPP( c_COMBC
% 0.99/1.62 ( X, tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 0.99/1.62 c_Polynomial_OpCons( X ) ), c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) ) ) ) ), hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ), Y ) ) ), Z ) }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.62 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.62 ( X ), U = T, Z = Y, ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP
% 0.99/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.99/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.62 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), ! U = T }.
% 0.99/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.62 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), ! Z = Y }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.62 ( X ), U ), T ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y )
% 0.99/1.62 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.62 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 0.99/1.62 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y ) ), Z ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.62 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T
% 0.99/1.62 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.62 ( X ), T ), Z ) ), Y ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.99/1.62 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T, hAPP(
% 0.99/1.62 hAPP( c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y
% 0.99/1.62 ), hAPP( hAPP( hAPP( c_If( W ), hAPP( c_fequal( Y ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), U ),
% 0.99/1.62 c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.99/1.62 Z, hAPP( hAPP( c_Polynomial_OpCons( X ), U ), T ) ) = hAPP( hAPP( hAPP( Z
% 0.99/1.62 , U ), T ), c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.99/1.62 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.62 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.99/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.99/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.99/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.62 ( X ), ! Z = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.62 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 = Y }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.62 = Y }.
% 0.99/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.62 ( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), U = Z, T = Y }.
% 0.99/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.62 ( X ), ! U = Z, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP
% 0.99/1.62 ( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.99/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.62 ( X ), ! T = Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP
% 0.99/1.62 ( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.99/1.62 { ! class_Rings_Osemiring( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 0.99/1.62 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP(
% 0.99/1.62 hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), T ) ), Y ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ), Z ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) = c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.62 ( X ), Y ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 = Y }.
% 0.99/1.62 { ! class_Groups_Omonoid__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.62 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.99/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Y ), Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) = hAPP
% 0.99/1.62 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) }.
% 0.99/1.62 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.62 = Y }.
% 0.99/1.62 { ! class_Groups_Omonoid__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.62 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) = Y }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), !
% 0.99/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ),
% 0.99/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = hAPP( hAPP(
% 0.99/1.62 c_Polynomial_OpCons( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OAbs__poly( X, hAPP( c_COMBK( X
% 0.99/1.62 , tc_Nat_Onat ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__ring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_OpCons( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z )
% 0.99/1.62 ), hAPP( hAPP( c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X )
% 0.99/1.62 ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.99/1.62 c_Polynomial_Osynthetic__div( X, Y, Z ) ) ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_OpCons( X ), hAPP( c_Polynomial_Opoly( X, Y ), Z ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.99/1.62 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.62 ( X ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone( X ) ) )
% 0.99/1.62 , Y ) }.
% 0.99/1.62 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.99/1.62 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y = hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone( X ) ) }
% 0.99/1.62 .
% 0.99/1.62 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.99/1.62 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.62 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y = hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.99/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.62 ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = Y }.
% 0.99/1.62 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.99/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.62 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.99/1.62 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ), Y = hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), ! Y = hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ), Z = hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.62 ( X ), Z ) = Y, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) = Z }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.62 ( X ), Y ) = Z, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) = Y }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.62 ( X ), Z ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ), Z = Y }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = Y, hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) = hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.99/1.62 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.99/1.62 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.99/1.62 { ! class_Groups_Oab__group__add( X ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ),
% 0.99/1.62 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ), Y ) }.
% 0.99/1.62 { ! class_Groups_Oab__group__add( X ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP( c_Polynomial_OpCons( X
% 0.99/1.62 ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Oab__group__add( X ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP( c_Polynomial_OpCons( X
% 0.99/1.62 ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.62 ), c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.62 }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.99/1.62 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) = hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.62 ( X ), Y ) }.
% 0.99/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y = hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ), Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), Y = hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.62 ( X ), Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.62 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) = Y, Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.62 X ), Y ) = Y }.
% 0.99/1.62 { ! class_Rings_Ocomm__ring( X ), hAPP( hAPP( c_Polynomial_Osmult( X ),
% 0.99/1.62 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) = hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_Osmult( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Z ) ), Y ) =
% 0.99/1.62 hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP( c_Polynomial_Opoly( X
% 0.99/1.62 , Z ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Oab__group__add( X ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.62 X ), Z ) ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.62 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP
% 0.99/1.62 ( c_Groups_Oplus__class_Oplus( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.62 ( X ), Y ) ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ) }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.62 ( X ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) ) = Y }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.62 ( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = Y }.
% 0.99/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.62 = Y }.
% 0.99/1.62 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.62 = Y }.
% 0.99/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.99/1.62 = Y }.
% 0.99/1.62 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.99/1.62 = Y }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.99/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, Y ) =
% 0.99/1.62 c_Polynomial_OAbs__poly( X, hAPP( c_COMBC( tc_Nat_Onat, X, X, hAPP(
% 0.99/1.62 c_COMBC( tc_Nat_Onat, X, tc_fun( X, X ), hAPP( hAPP( c_COMBB(
% 0.99/1.62 tc_HOL_Obool, tc_fun( X, tc_fun( X, X ) ), tc_Nat_Onat ), c_If( X ) ),
% 0.99/1.62 c_fequal( Y ) ) ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ),
% 0.99/1.62 c_Groups_Oone__class_Oone( X ) ), c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) ) }.
% 0.99/1.62 { ! class_Rings_Oring( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ),
% 0.99/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Oring( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ),
% 0.99/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.62 ( X ), Z ) ), Y ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.62 ( X ), Z ) ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP(
% 0.99/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.62 ( X ), Z ) ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP(
% 0.99/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.99/1.62 , hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.99/1.62 , hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.99/1.62 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.99/1.62 Z = Y, Z = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), ! Z = hAPP( c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.62 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP
% 0.99/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.99/1.62 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.99/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.62 = Y }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.99/1.62 = Y }.
% 0.99/1.62 { ! class_Groups_Oab__group__add( X ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__ring( X ), hAPP( hAPP( c_Polynomial_Osmult( X ), Z )
% 0.99/1.62 , hAPP( c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y )
% 0.99/1.62 ) = hAPP( c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ),
% 0.99/1.62 hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.62 ( X ), Y ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( X ) }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( X ), Z = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.62 ( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.62 X ), Y ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) = Y }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 0.99/1.62 ), c_Groups_Oone__class_Oone( X ) ), Y ) = Y }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.62 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 0.99/1.62 , Z ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), c_Groups_Oone__class_Oone( X ) ) )
% 0.99/1.62 , Y ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.62 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 0.99/1.62 ), T ), c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP
% 0.99/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.99/1.62 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 0.99/1.62 c_Polynomial_Omonom( X, T, Z ) ), c_Polynomial_Omonom( X, Y, Z ) ) =
% 0.99/1.62 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T )
% 0.99/1.62 , Y ), Z ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.99/1.62 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.99/1.62 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.99/1.62 ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), Y )
% 0.99/1.62 ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.99/1.62 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Oab__semigroup__add( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.62 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T
% 0.99/1.62 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 0.99/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y, hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ) }.
% 0.99/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Z ), T = Y }.
% 0.99/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y, hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) }.
% 0.99/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 0.99/1.62 { ! class_Groups_Ocancel__ab__semigroup__add( X ), ! hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 0.99/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), T ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), T ), Z = Y }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( X ), Y = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) }.
% 0.99/1.62 { ! class_Groups_Ogroup__add( X ), ! Y = hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( X ) }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_OpCons( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y )
% 0.99/1.62 ), hAPP( hAPP( c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X )
% 0.99/1.62 ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Z ) )
% 0.99/1.62 }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ),
% 0.99/1.62 hAPP( c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.62 }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), Z ),
% 0.99/1.62 hAPP( hAPP( c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ),
% 0.99/1.62 hAPP( c_Polynomial_Opoly( X, Y ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.62 X ), Z ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) = c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.99/1.62 X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.99/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.99/1.62 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 0.99/1.62 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 0.99/1.62 X, Z ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Ouminus( X ), hAPP( hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.62 ( tc_fun( T, X ) ), Z ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 0.99/1.62 , hAPP( Z, Y ) ) }.
% 0.99/1.62 { ! class_Rings_Oidom( t_a ),
% 0.99/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( t_a, t_a,
% 0.99/1.62 c_Polynomial_Opoly( t_a, v_cs____ ) ), ! skol4 =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( t_a ) }.
% 0.99/1.62 { ! class_Rings_Oidom( t_a ),
% 0.99/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( t_a, t_a,
% 0.99/1.62 c_Polynomial_Opoly( t_a, v_cs____ ) ), alpha31( skol4 ) }.
% 0.99/1.62 { ! alpha31( X ), ! skol5( Y ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.62 }.
% 0.99/1.62 { ! alpha31( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.99/1.62 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.99/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, skol30( X ) ) ),
% 0.99/1.62 skol5( X ) ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 0.99/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, v_cs____ ) }.
% 0.99/1.62 { ! alpha31( X ), hAPP( c_Polynomial_Opoly( t_a, v_cs____ ), Y ) = hAPP(
% 0.99/1.62 hAPP( c_Groups_Oplus__class_Oplus( t_a ), hAPP( c_Polynomial_Opoly( t_a,
% 0.99/1.62 v_cs____ ), c_Groups_Ozero__class_Ozero( t_a ) ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( t_a ), Y ), skol5( X ) ) ), hAPP(
% 0.99/1.62 c_Polynomial_Opoly( t_a, hAPP( hAPP( c_Polynomial_OpCons( t_a ), X ),
% 0.99/1.62 skol30( X ) ) ), Y ) ) ) }.
% 0.99/1.62 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.99/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, Z ) ), Y ) ),
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 0.99/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, v_cs____ ), !
% 0.99/1.62 hAPP( c_Polynomial_Opoly( t_a, v_cs____ ), skol37( X, Y, Z ) ) = hAPP(
% 0.99/1.62 hAPP( c_Groups_Oplus__class_Oplus( t_a ), hAPP( c_Polynomial_Opoly( t_a,
% 0.99/1.62 v_cs____ ), c_Groups_Ozero__class_Ozero( t_a ) ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( t_a ), skol37( X, Y, Z ) ), Y ) ), hAPP(
% 0.99/1.62 c_Polynomial_Opoly( t_a, hAPP( hAPP( c_Polynomial_OpCons( t_a ), X ), Z )
% 0.99/1.62 ), skol37( X, Y, Z ) ) ) ), alpha31( X ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semiring__1( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , U ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), W ) ), ! hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), U ), W ) = c_Groups_Oone__class_Oone( X
% 0.99/1.62 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), W ), T ) ) ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Z ), Y ) =
% 0.99/1.62 c_Polynomial_OAbs__poly( X, hAPP( hAPP( c_COMBS( tc_Nat_Onat, X, X ),
% 0.99/1.62 hAPP( hAPP( c_COMBB( X, tc_fun( X, X ), tc_Nat_Onat ),
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ) ), c_Polynomial_Ocoeff( X, Z ) ) ),
% 0.99/1.62 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 0.99/1.62 ), Z ), Y ) = c_Polynomial_OAbs__poly( X, hAPP( hAPP( c_COMBB( X, X,
% 0.99/1.62 tc_Nat_Onat ), hAPP( c_Groups_Otimes__class_Otimes( X ), Z ) ),
% 0.99/1.62 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) )
% 0.99/1.62 }.
% 0.99/1.62 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP
% 0.99/1.62 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.99/1.62 tc_Nat_Onat ) ) = Y }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.99/1.62 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.99/1.62 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.99/1.62 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 0.99/1.62 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol6( X
% 0.99/1.62 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol6( X, Y, Z ) ), Z = Y
% 0.99/1.62 }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 0.99/1.62 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 0.99/1.62 c_Polynomial_Ocoeff( X, Y ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), Y ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Lattices_Oboolean__algebra( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) ) }.
% 0.99/1.62 { ! class_Lattices_Oboolean__algebra( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.99/1.62 { ! class_Lattices_Oboolean__algebra( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) )
% 0.99/1.62 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), T ), Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 0.99/1.62 ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), Z ), T ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 0.99/1.62 ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), Y ), T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z
% 0.99/1.62 ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), U ), T ) ), hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.62 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T
% 0.99/1.62 ) ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), c_Groups_Oone__class_Oone( X ) ), Y ) ) }
% 0.99/1.62 .
% 0.99/1.62 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.62 ( X ), Y ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y
% 0.99/1.62 ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.62 ( X ), Y ) ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 0.99/1.62 , Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y
% 0.99/1.62 ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 0.99/1.62 , Z ) ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Z ) ), Y ) =
% 0.99/1.62 hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP( c_Polynomial_Ocoeff( X
% 0.99/1.62 , Z ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.62 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.62 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), T ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), U ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), T ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.62 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.62 ( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.62 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.62 ( c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Z ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Y ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Y ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_Osmult( X ), T ), Z ) ), Y ) ), hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), hBOOL(
% 0.99/1.62 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ),
% 0.99/1.62 hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Y ) ) ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_OAbs__poly( X,
% 0.99/1.62 c_Polynomial_Ocoeff( X, Y ) ) = Y }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.99/1.62 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), hAPP(
% 0.99/1.62 hAPP( c_Polynomial_OpCons( X ), Z ), hAPP( hAPP( c_Polynomial_OpCons( X )
% 0.99/1.62 , c_Groups_Oone__class_Oone( X ) ), c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 0.99/1.62 ( X ) }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.99/1.62 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 0.99/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), T =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.99/1.62 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.99/1.62 X ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 0.99/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.99/1.62 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 0.99/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), Z =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), T ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.99/1.62 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.99/1.62 X ), T ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 0.99/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.62 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.99/1.62 ( tc_Polynomial_Opoly( X ) ), T ), hAPP( hAPP( c_Polynomial_Osmult( X ),
% 0.99/1.62 Z ), Y ) ) ), Z = c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 0.99/1.62 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.99/1.62 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), T = c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.99/1.62 X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z ) ), Y ) ) }.
% 0.99/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 0.99/1.62 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 0.99/1.62 hAPP( hAPP( c_Polynomial_Osmult( X ), Y ), Z ) ) ), hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Z ) ) }.
% 0.99/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 0.99/1.62 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 0.99/1.62 Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.99/1.62 X ) ), T ), hAPP( hAPP( c_Polynomial_Osmult( X ), Y ), Z ) ) ) }.
% 0.99/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.62 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.62 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.99/1.62 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.62 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.99/1.62 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.99/1.62 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.99/1.62 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, T ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.62 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) ) }.
% 0.99/1.62 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, T ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.62 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) ) }.
% 0.99/1.62 { ! class_Rings_Oordered__comm__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.99/1.62 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.99/1.62 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.99/1.62 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.62 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.62 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ), alpha1( X, Y, Z ), alpha18( X, Y, Z
% 0.99/1.62 ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z ), hBOOL
% 0.99/1.62 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha18( X, Y, Z ), hBOOL
% 0.99/1.62 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.62 { ! alpha18( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.62 { ! alpha18( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Y ) ), alpha18( X, Y, Z ) }.
% 0.99/1.62 { ! alpha1( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 0.99/1.62 { ! alpha1( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y
% 0.99/1.62 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.62 ) ) ), alpha1( X, Y, Z ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), alpha2( X
% 0.99/1.62 , Y, Z ), alpha19( X, Y, Z ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ), hBOOL
% 0.99/1.62 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha19( X, Y, Z ), hBOOL
% 0.99/1.62 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.99/1.62 { ! alpha19( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.62 { ! alpha19( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 Y ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.62 ) ) ), alpha19( X, Y, Z ) }.
% 0.99/1.62 { ! alpha2( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 0.99/1.62 { ! alpha2( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Y ) ), alpha2( X, Y, Z ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__ring( X ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.62 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( X ) ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) )
% 0.99/1.62 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) )
% 0.99/1.62 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( X ), Z = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.62 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.99/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.62 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( X ) ) ) }.
% 0.99/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ), hBOOL( hAPP
% 0.99/1.62 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.62 ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.99/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Y ) ) }.
% 0.99/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( X ) ) ) }.
% 0.99/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Y ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.62 ) ) ) }.
% 0.99/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.62 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.62 ) ) ) }.
% 0.99/1.62 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.62 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.62 ( X ), Y ) ) ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP( hAPP(
% 0.99/1.62 c_Polynomial_OpCons( X ), Z ), Y ) ), c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ) ) = Z }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.99/1.62 ( hAPP( c_Polynomial_Osmult( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 0.99/1.62 ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.99/1.62 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 0.99/1.62 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.99/1.62 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.62 }.
% 0.99/1.62 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.99/1.62 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T )
% 0.99/1.62 , Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP(
% 0.99/1.62 c_Polynomial_Ocoeff( X, T ), Y ) ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 0.99/1.62 ) ) }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.99/1.62 c_Polynomial_Oorder( X, Z, Y ) ) ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Oab__group__add( X ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.99/1.62 c_Polynomial_OAbs__poly( X, hAPP( hAPP( c_COMBB( X, X, tc_Nat_Onat ),
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ) ), c_Polynomial_Ocoeff( X, Y ) ) ) }
% 0.99/1.62 .
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 0.99/1.62 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.99/1.62 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ),
% 0.99/1.62 Z ) ), Y ) ), alpha3( X, Y, T ) }.
% 0.99/1.62 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.99/1.62 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ),
% 0.99/1.62 Z ) ), Y ) ), alpha20( X, Y, Z, T ) }.
% 0.99/1.62 { ! class_Fields_Ofield( X ), ! alpha3( X, Y, T ), ! alpha20( X, Y, Z, T )
% 0.99/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.99/1.62 , hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z ) ), Y ) ) }.
% 0.99/1.62 { ! alpha20( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.99/1.62 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.99/1.62 ) ) }.
% 0.99/1.62 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha20( X, Y, Z, T ) }.
% 0.99/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.99/1.62 , Z ), Y ) ), alpha20( X, Y, Z, T ) }.
% 0.99/1.62 { ! alpha3( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.62 { Z = c_Groups_Ozero__class_Ozero( X ), alpha3( X, Y, Z ) }.
% 0.99/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha3( X
% 0.99/1.62 , Y, Z ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ), Z = c_Groups_Ozero__class_Ozero( X
% 0.99/1.62 ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ), Y = c_Groups_Ozero__class_Ozero( X
% 0.99/1.62 ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.62 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__ring( X ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Oone__class_Oone( X )
% 0.99/1.62 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Oone__class_Oone( X )
% 0.99/1.62 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) ) }.
% 0.99/1.62 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.99/1.62 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.99/1.62 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.99/1.62 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.99/1.62 { ! class_Lattices_Oboolean__algebra( X ), ! hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) = hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ), Z = Y }.
% 0.99/1.62 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y, hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) = hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.99/1.62 { ! class_Groups_Ouminus( X ), hAPP( hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.62 ( tc_fun( T, X ) ), Z ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 0.99/1.62 , hAPP( Z, Y ) ) }.
% 0.99/1.62 { ! class_Lattices_Oboolean__algebra( X ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = Y }.
% 0.99/1.62 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.99/1.62 ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.62 ( X ), c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.62 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.62 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.99/1.62 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.99/1.62 hAPP( Z, skol7( U, W, Z ) ) ) }.
% 0.99/1.62 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.99/1.62 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.99/1.62 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), skol7( X, Y, Z ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ) ) ) }.
% 0.99/1.62 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.99/1.62 hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( X ), T ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL( hAPP( Z, hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), skol31( X, Y, Z ) ) ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP
% 0.99/1.62 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.62 ), T ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ),
% 0.99/1.62 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ) ) }.
% 0.99/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.99/1.62 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.99/1.62 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.99/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.62 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.99/1.62 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.99/1.62 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.99/1.62 .
% 0.99/1.62 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.99/1.62 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.99/1.62 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ) }.
% 0.99/1.62 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.99/1.62 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.99/1.62 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.99/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ), Y
% 0.99/1.62 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.99/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.99/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP
% 0.99/1.62 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), hAPP(
% 0.99/1.62 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ), hBOOL( hAPP
% 0.99/1.62 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) )
% 0.99/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), hAPP(
% 0.99/1.62 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ) }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ), X ) = hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.62 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.99/1.62 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.99/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.99/1.62 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.99/1.62 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP
% 0.99/1.62 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), U ), T ) ) ), hBOOL(
% 0.99/1.62 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), U ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), T ) ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.99/1.62 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP
% 0.99/1.62 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), U ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), T ) ) ),
% 0.99/1.62 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP(
% 0.99/1.62 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), U ), T ) ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 0.99/1.62 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), Z =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 0.99/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.62 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.99/1.62 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.99/1.62 ( X ) }.
% 0.99/1.62 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.62 = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.62 X ), Z ), T ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T )
% 0.99/1.62 ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.62 hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U ), T ) ), hBOOL( hAPP(
% 0.99/1.62 hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), U ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) ) ) }.
% 0.99/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.99/1.62 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.62 X ), T ), Z ) ), Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.99/1.62 ( tc_Nat_Onat, U ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 0.99/1.62 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), U ) ), Y ) ) }.
% 0.99/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.99/1.62 tc_Nat_Onat ) ) = Y }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.62 , Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) ) ) }.
% 0.99/1.62 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP
% 0.99/1.62 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) )
% 0.99/1.62 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) ) }.
% 0.99/1.62 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 0.99/1.62 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.99/1.62 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! class_Orderings_Opreorder( X ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( X, Y ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.99/1.62 c_Polynomial_Oorder( X, Z, Y ) ) ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.99/1.62 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), hAPP(
% 0.99/1.62 c_Nat_OSuc, c_Polynomial_Oorder( X, Z, Y ) ) ) ), Y ) ) }.
% 0.99/1.62 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.99/1.62 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.62 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP( hAPP(
% 0.99/1.62 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), hAPP(
% 0.99/1.62 c_Nat_OSuc, c_Polynomial_Oorder( X, Z, Y ) ) ) ), Y ) ) }.
% 0.99/1.62 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.99/1.62 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.62 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.99/1.62 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP(
% 0.99/1.62 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( hAPP
% 0.99/1.62 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.62 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ), X = Y }.
% 0.99/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.99/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) ), hBOOL( hAPP(
% 0.99/1.62 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.99/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ), X ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ), X ) ), hBOOL( hAPP
% 0.99/1.62 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.99/1.62 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 0.99/1.62 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.62 c_Nat_OSuc, Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.99/1.62 ( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 0.99/1.62 ( c_Nat_OSuc, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.62 tc_Nat_Onat, Y ), X ) ), Y = hAPP( c_Nat_OSuc, X ) }.
% 0.99/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.62 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 0.99/1.62 ( c_Nat_OSuc, X ) ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.62 c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.62 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.62 c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 0.99/1.62 ( c_Nat_OSuc, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.62 tc_Nat_Onat, Y ), X ) ), Y = hAPP( c_Nat_OSuc, X ) }.
% 0.99/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.62 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 0.99/1.62 ( c_Nat_OSuc, X ) ) ) }.
% 0.99/1.62 { ! Y = hAPP( c_Nat_OSuc, X ), hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP( c_Nat_OSuc, X
% 0.99/1.62 ) ) ) }.
% 0.99/1.62 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.62 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.62 c_Nat_OSuc, X ) ), Y ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.62 c_Nat_OSuc, X ) ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.62 c_Nat_OSuc, X ) ), X ) ) }.
% 0.99/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 0.99/1.62 c_Nat_OSuc, Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.62 tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), X ), Y = X }.
% 0.99/1.62 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 0.99/1.62 c_Nat_OSuc, Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.62 tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), X ) }.
% 0.99/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), hAPP(
% 0.99/1.62 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X = hAPP(
% 0.99/1.62 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.62 { ! X = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.99/1.62 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), hAPP(
% 0.99/1.62 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.62 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), hAPP( c_Nat_OSuc, X )
% 0.99/1.62 ) = hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y
% 0.99/1.62 ), X ) ) }.
% 0.99/1.62 { ! hAPP( c_Nat_OSuc, Y ) = hAPP( c_Nat_OSuc, X ), Y = X }.
% 0.99/1.62 { ! hAPP( c_Nat_OSuc, Y ) = hAPP( c_Nat_OSuc, X ), Y = X }.
% 0.99/1.62 { ! Y = X, hAPP( c_Nat_OSuc, Y ) = hAPP( c_Nat_OSuc, X ) }.
% 0.99/1.62 { ! hAPP( c_Nat_OSuc, X ) = X }.
% 0.99/1.62 { ! X = hAPP( c_Nat_OSuc, X ) }.
% 0.99/1.62 { ! hAPP( c_Nat_OSuc, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Nat_OSuc, X ) }.
% 0.99/1.62 { ! hAPP( c_Nat_OSuc, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! hAPP( c_Nat_OSuc, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Nat_OSuc, X ) }.
% 0.99/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Nat_OSuc, X ) }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( c_Nat_OSuc
% 0.99/1.62 , Y ) ), X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y
% 0.99/1.62 ), hAPP( c_Nat_OSuc, X ) ) }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( c_Nat_OSuc
% 0.99/1.62 , Y ) ), X ) = hAPP( c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.62 ( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), hAPP(
% 0.99/1.62 c_Nat_OSuc, X ) ) = hAPP( c_Nat_OSuc, hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.62 { hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) = hAPP(
% 0.99/1.62 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.99/1.62 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.62 { hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) = X }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP(
% 0.99/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ), X ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) = X }.
% 0.99/1.62 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) = X }.
% 0.99/1.62 { hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.62 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.99/1.62 tc_Int_Oint ) ), X ) ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 0.99/1.62 }.
% 0.99/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.99/1.62 ( tc_Int_Oint ) }.
% 0.99/1.62 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), hAPP( c_Nat_OSuc
% 0.99/1.62 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = hAPP( c_Nat_OSuc
% 0.99/1.62 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.62 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.62 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( c_Nat_OSuc,
% 0.99/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = hAPP( c_Nat_OSuc
% 0.99/1.62 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.62 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.99/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.99/1.62 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.62 { ! hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = hAPP(
% 0.99/1.62 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), alpha4( X, Y
% 0.99/1.62 ), alpha21( X, Y ) }.
% 0.99/1.62 { ! alpha4( X, Y ), hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 0.99/1.62 , Y ), X ) }.
% 0.99/1.62 { ! alpha21( X, Y ), hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 0.99/1.62 , Y ), X ) }.
% 0.99/1.62 { ! alpha21( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.62 { ! alpha21( X, Y ), X = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.99/1.62 tc_Nat_Onat ) ) }.
% 0.99/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = hAPP( c_Nat_OSuc
% 0.99/1.63 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha21( X, Y ) }.
% 0.99/1.63 { ! alpha4( X, Y ), Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ) }.
% 0.99/1.63 { ! alpha4( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X
% 0.99/1.63 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha4( X, Y ) }.
% 0.99/1.63 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.99/1.63 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha5( X, Y
% 0.99/1.63 ), alpha22( X, Y ) }.
% 0.99/1.63 { ! alpha5( X, Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 0.99/1.63 , Y ), X ) = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! alpha22( X, Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 0.99/1.63 , Y ), X ) = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! alpha22( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! alpha22( X, Y ), X = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ) }.
% 0.99/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = hAPP( c_Nat_OSuc
% 0.99/1.63 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha22( X, Y ) }.
% 0.99/1.63 { ! alpha5( X, Y ), Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ) }.
% 0.99/1.63 { ! alpha5( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X
% 0.99/1.63 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha5( X, Y ) }.
% 0.99/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.63 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = hAPP
% 0.99/1.63 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.63 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = hAPP
% 0.99/1.63 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.63 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X
% 0.99/1.63 = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.99/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP(
% 0.99/1.63 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.63 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( c_Nat_OSuc,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), hAPP(
% 0.99/1.63 c_Nat_OSuc, X ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.99/1.63 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X
% 0.99/1.63 ) ) }.
% 0.99/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 0.99/1.63 c_Nat_OSuc, Y ) ), X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.63 tc_Nat_Onat ), X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.63 tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ),
% 0.99/1.63 Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 0.99/1.63 c_Nat_OSuc, Z ) ), X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ),
% 0.99/1.63 Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 0.99/1.63 c_Nat_OSuc, Z ) ), X ) ) ) }.
% 0.99/1.63 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.63 hAPP( c_Nat_OSuc, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) }.
% 0.99/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) }.
% 0.99/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) = hAPP(
% 0.99/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) = hAPP(
% 0.99/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.99/1.63 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.99/1.63 , Z ), hAPP( c_Nat_OSuc, Y ) ) = hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.63 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.63 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.63 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), !
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.63 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), hBOOL
% 0.99/1.63 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 0.99/1.63 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.63 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), hBOOL
% 0.99/1.63 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 0.99/1.63 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.99/1.63 { hAPP( c_Nat_OSuc, X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.63 tc_Nat_Onat ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.99/1.63 { hAPP( c_Nat_OSuc, X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.63 tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.99/1.63 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP( hAPP(
% 0.99/1.63 c_Polynomial_OpCons( X ), T ), Z ) ), hAPP( c_Nat_OSuc, Y ) ) = hAPP(
% 0.99/1.63 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, T ) ) = hAPP(
% 0.99/1.63 hAPP( c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, T ) ), !
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 , Y ) ), Z = Y }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, T ) ) ), hAPP(
% 0.99/1.63 hAPP( c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, T ) ) ) )
% 0.99/1.63 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.99/1.63 , Z ), hAPP( c_Nat_OSuc, hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y )
% 0.99/1.63 , hAPP( c_Nat_OSuc, hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ) ) ), Z = Y, Z = hAPP( c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.63 ), Y ) }.
% 0.99/1.63 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, hAPP(
% 0.99/1.63 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.99/1.63 ( c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, hAPP(
% 0.99/1.63 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.63 { ! class_Rings_Oidom( X ), ! Z = hAPP( c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.63 ), Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), hAPP(
% 0.99/1.63 c_Nat_OSuc, hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.63 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), hAPP(
% 0.99/1.63 c_Nat_OSuc, hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.63 ) ) ) }.
% 0.99/1.63 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 0.99/1.63 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Y = Z }.
% 0.99/1.63 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Z = Y }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Z = T, hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Y = T, hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! Z = Y, ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Oord( X ), ! Z = Y, ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Y = Z }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Y = Z, hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 0.99/1.63 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! class_Orderings_Opreorder( X ), ! Z = Y, hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Z = Y }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 0.99/1.63 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, skol8( X, Y, Z ) ) ), hAPP
% 0.99/1.63 ( Y, skol8( X, Y, Z ) ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ) }.
% 0.99/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, hAPP( c_Nat_OSuc, Y
% 0.99/1.63 ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ), c_Groups_Ozero__class_Ozero
% 0.99/1.63 ( X ) ), c_Polynomial_Omonom( X, Z, Y ) ) }.
% 0.99/1.63 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = hAPP(
% 0.99/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) }.
% 0.99/1.63 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.63 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.99/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.63 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) = hAPP
% 0.99/1.63 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y = X }.
% 0.99/1.63 { ! Y = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 0.99/1.63 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) }.
% 0.99/1.63 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) = hAPP
% 0.99/1.63 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ), Z = X }.
% 0.99/1.63 { ! Z = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 0.99/1.63 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), hAPP(
% 0.99/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ), hBOOL(
% 0.99/1.63 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), hAPP(
% 0.99/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), X ) ) }
% 0.99/1.63 .
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ) }
% 0.99/1.63 .
% 0.99/1.63 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 0.99/1.63 , X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y )
% 0.99/1.63 ), Y = X }.
% 0.99/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.99/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.99/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.99/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X =
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.63 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.99/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone(
% 0.99/1.63 tc_Nat_Onat ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 0.99/1.63 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, Z ) ) ), Y ) )
% 0.99/1.63 }.
% 0.99/1.63 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) = X }.
% 0.99/1.63 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.99/1.63 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = Y, X
% 0.99/1.63 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.99/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.99/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.99/1.63 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.99/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.99/1.63 .
% 0.99/1.63 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.99/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.99/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.99/1.63 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.99/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.99/1.63 .
% 0.99/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP(
% 0.99/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP(
% 0.99/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), skol9
% 0.99/1.63 ( X, Y ) ) }.
% 0.99/1.63 { ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 0.99/1.63 .
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 0.99/1.63 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 0.99/1.63 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), T ) ), hAPP( hAPP
% 0.99/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL(
% 0.99/1.63 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), X ) ), hBOOL(
% 0.99/1.63 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL(
% 0.99/1.63 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL(
% 0.99/1.63 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.99/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP
% 0.99/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), hAPP(
% 0.99/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), hAPP(
% 0.99/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ) ), hAPP(
% 0.99/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.99/1.63 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.63 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.63 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.99/1.63 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.99/1.63 , Y ), X ) }.
% 0.99/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.99/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.99/1.63 tc_Nat_Onat ) }.
% 0.99/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.99/1.63 tc_Nat_Onat ) }.
% 0.99/1.63 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.63 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Z, Y ) =
% 0.99/1.63 c_Orderings_Oord__class_OLeast( tc_Nat_Onat, hAPP( hAPP( c_COMBB(
% 0.99/1.63 tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat ), c_fNot ), hAPP( c_COMBC(
% 0.99/1.63 tc_Nat_Onat, tc_Polynomial_Opoly( X ), tc_HOL_Obool, hAPP( hAPP( c_COMBB
% 0.99/1.63 ( tc_Polynomial_Opoly( X ), tc_fun( tc_Polynomial_Opoly( X ),
% 0.99/1.63 tc_HOL_Obool ), tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP( c_COMBB( tc_Nat_Onat,
% 0.99/1.63 tc_Polynomial_Opoly( X ), tc_Nat_Onat ), hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.99/1.63 c_Polynomial_OpCons( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z )
% 0.99/1.63 ), hAPP( hAPP( c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X )
% 0.99/1.63 ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ) ),
% 0.99/1.63 c_Nat_OSuc ) ) ), Y ) ) ) }.
% 0.99/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.99/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ), hBOOL( hAPP(
% 0.99/1.63 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.99/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.99/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.99/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 0.99/1.63 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ), Y =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.99/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ) }.
% 0.99/1.63 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), X ) ) = hAPP(
% 0.99/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), Y ) ), Z ) ), X ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 0.99/1.63 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), X ) ) }
% 0.99/1.63 .
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.99/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.99/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.99/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.99/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.99/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.99/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.99/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.99/1.63 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.99/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.99/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.99/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.99/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.99/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.99/1.63 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.99/1.63 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.99/1.63 ), Z ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.99/1.63 , ! X = Z, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.99/1.63 Z ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.99/1.63 , ! X = Y }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.99/1.63 , ! Y = X }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.99/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.99/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.99/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.99/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.99/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.99/1.63 , ! Y = X }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.99/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.99/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.99/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.99/1.63 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.99/1.63 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.99/1.63 ), X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.99/1.63 ), Z ) ) }.
% 0.99/1.63 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.99/1.63 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.99/1.63 ), X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.99/1.63 Z ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.99/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.99/1.63 ), Y = X }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.99/1.63 ), Y = X }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.99/1.63 ), Z ) ) }.
% 0.99/1.63 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.99/1.63 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.99/1.63 ), Z ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.99/1.63 , X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.99/1.63 ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , Y = X }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.99/1.63 ), Y = X }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.99/1.63 ), X = Y }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , ! X = Y, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.99/1.63 ), Y ) ) }.
% 0.99/1.63 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.99/1.63 , X ) ) }.
% 0.99/1.63 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.99/1.63 , X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.99/1.63 , X ) ) }.
% 0.99/1.63 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.99/1.63 , X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.99/1.63 ), Y ) ) }.
% 0.99/1.63 { ! alpha6( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.99/1.63 tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.63 { ! alpha6( X, Y ), ! Y = X }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , Y = X, alpha6( X, Y ) }.
% 0.99/1.63 { ! alpha6( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.99/1.63 tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.63 { ! alpha6( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.99/1.63 tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.99/1.63 , alpha6( X, Y ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , alpha7( X, Y ), Y = X }.
% 0.99/1.63 { ! alpha7( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.99/1.63 tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.63 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.99/1.63 , X ) ) }.
% 0.99/1.63 { ! alpha7( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.99/1.63 tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.63 { ! alpha7( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.99/1.63 tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.99/1.63 , alpha7( X, Y ) }.
% 0.99/1.63 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.99/1.63 , X ) ) }.
% 0.99/1.63 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X )
% 0.99/1.63 , Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.99/1.63 ), Y = X }.
% 0.99/1.63 { ! class_Orderings_Owellorder( X ), ! hBOOL( hAPP( Y, Z ) ), hBOOL( hAPP(
% 0.99/1.63 Y, c_Orderings_Oord__class_OLeast( X, Y ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.99/1.63 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y )
% 0.99/1.63 ), Y = X }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.99/1.63 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Z )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), Z )
% 0.99/1.63 ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ) }
% 0.99/1.63 .
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), X ) ) }
% 0.99/1.63 .
% 0.99/1.63 { ! class_Orderings_Owellorder( X ), ! hBOOL( hAPP( Y, Z ) ), hBOOL( hAPP(
% 0.99/1.63 Y, c_Orderings_Oord__class_OLeast( X, Y ) ) ) }.
% 0.99/1.63 { ! class_Orderings_Owellorder( X ), ! hBOOL( hAPP( Z, Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Orderings_Oord__class_OLeast( X,
% 0.99/1.63 Z ) ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.99/1.63 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ), Y =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.99/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.99/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.99/1.63 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.99/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.99/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.99/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.99/1.63 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Ozero__class_Ozero
% 0.99/1.63 ( tc_Int_Oint ) ) ) }.
% 0.99/1.63 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ) ), c_Orderings_Oord__class_OLeast( tc_Nat_Onat, X ) =
% 0.99/1.63 hAPP( c_Nat_OSuc, c_Orderings_Oord__class_OLeast( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.63 ( c_COMBB( tc_Nat_Onat, tc_HOL_Obool, tc_Nat_Onat ), X ), c_Nat_OSuc ) )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.99/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), Z =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.99/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.63 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.99/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.99/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.99/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.99/1.63 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.99/1.63 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.99/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.99/1.63 .
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oone__class_Oone(
% 0.99/1.63 tc_Int_Oint ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 0.99/1.63 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 0.99/1.63 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), skol10
% 0.99/1.63 ( X, Y ) ) }.
% 0.99/1.63 { ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 0.99/1.63 .
% 0.99/1.63 { ! class_Groups_Ozero( X ), hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y )
% 0.99/1.63 = c_Polynomial_OAbs__poly( X, c_Nat_Onat_Onat__case( X, Z,
% 0.99/1.63 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 0.99/1.63 { hAPP( c_Nat_Onat_Onat__case( Z, Y, X ), c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ) = Y }.
% 0.99/1.63 { hAPP( c_Nat_Onat_Onat__case( T, Z, Y ), hAPP( c_Nat_OSuc, X ) ) = hAPP( Y
% 0.99/1.63 , X ) }.
% 0.99/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Ocoeff( X, hAPP( hAPP(
% 0.99/1.63 c_Polynomial_OpCons( X ), Z ), Y ) ) = c_Nat_Onat_Onat__case( X, Z,
% 0.99/1.63 c_Polynomial_Ocoeff( X, Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.63 c_Nat_OSuc, Y ) ), X ) ), hBOOL( hAPP( c_Nat_Onat_Onat__case(
% 0.99/1.63 tc_HOL_Obool, c_fFalse, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.99/1.63 ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Nat_Onat_Onat__case( tc_HOL_Obool, c_fFalse,
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ) ), X ) ), hBOOL( hAPP
% 0.99/1.63 ( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ) )
% 0.99/1.63 , X ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Omono( tc_Nat_Onat, X
% 0.99/1.63 , c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), ! hBOOL( hAPP( hAPP(
% 0.99/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), T ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ) ), hAPP( Y, Z ) ) ) }
% 0.99/1.63 .
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hAPP( c_Int_Onat, hAPP(
% 0.99/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) = hAPP(
% 0.99/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Int_Onat,
% 0.99/1.63 hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) ), hAPP(
% 0.99/1.63 c_Int_Onat, hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ) )
% 0.99/1.63 }.
% 0.99/1.63 { ! class_Rings_Olinordered__semiring__1__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, T ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 , U ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), W ) ), ! hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( X ), U ), W ) = c_Groups_Oone__class_Oone( X
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), W ), T ) ) ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP( c_Nat_OSuc,
% 0.99/1.63 hAPP( c_Int_Onat, X ) ) = hAPP( c_Int_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.99/1.63 tc_Int_Oint ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 0.99/1.63 , Y ) ), hAPP( c_Nat_OSuc, X ) ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP(
% 0.99/1.63 c_Nat_OSuc, X ) ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( c_Nat_OSuc, X ) ) ) }
% 0.99/1.63 .
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 0.99/1.63 .
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 0.99/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 0.99/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.63 { alpha32( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.63 tc_Nat_Onat, hAPP( c_Int_Onat, Y ) ), hAPP( c_Int_Onat, X ) ) ), hBOOL(
% 0.99/1.63 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }.
% 0.99/1.63 { alpha32( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.63 tc_Int_Oint, Y ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.63 tc_Nat_Onat, hAPP( c_Int_Onat, Y ) ), hAPP( c_Int_Onat, X ) ) ) }.
% 0.99/1.63 { ! alpha32( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 0.99/1.63 { ! alpha32( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha32( X, Y ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ),
% 0.99/1.63 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.63 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), hAPP
% 0.99/1.63 ( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( c_Int_Onat, X ) ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), hAPP( c_Int_Onat, X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.99/1.63 c_Int_Onat, Y ) ), hAPP( c_Int_Onat, X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Int_Oint ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.99/1.63 c_Int_Onat, Y ) ), hAPP( c_Int_Onat, X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, Y ) ), hAPP
% 0.99/1.63 ( c_Int_Onat, X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, Y ) ), hAPP
% 0.99/1.63 ( c_Int_Onat, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Int_Oint, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, Y ) ), hAPP
% 0.99/1.63 ( c_Int_Onat, X ) ) ) }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), T ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = T, hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 0.99/1.63 ( X, Z ), Y ) ), ! Y = T, hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.63 Z ), T ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! Z = Y, ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, T ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, T ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Oord( X ), ! Z = Y, ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), T ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Y = Z }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 0.99/1.63 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), Z = Y, hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), Y = Z }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Y = Z, ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), Z = Y }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), ! Z = Y, ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), Z = Y, hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), ! Z = Y }.
% 0.99/1.63 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.99/1.63 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP(
% 0.99/1.63 c_Int_Onat, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( c_Int_Onat, X ) ) )
% 0.99/1.63 }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), Z = Y, hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Z ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 0.99/1.63 .
% 0.99/1.63 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 0.99/1.63 , X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 0.99/1.63 .
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), Y
% 0.99/1.63 = X }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 0.99/1.63 .
% 0.99/1.63 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 0.99/1.63 , X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 0.99/1.63 .
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.63 Y = X }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), X ) ), hBOOL(
% 0.99/1.63 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.63 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), X ) = hAPP(
% 0.99/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 0.99/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 0.99/1.63 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.99/1.63 c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.99/1.63 c_Nat_OSuc, Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.99/1.63 c_Nat_OSuc, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Nat_Onat, Y ), X ) ), Y = X }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Z ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 0.99/1.63 , Y ) ), Z ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hAPP( c_Nat_OSuc, Y ) = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.99/1.63 c_Nat_OSuc, X ) ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.99/1.63 c_Nat_OSuc, X ) ) ), X = Y }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.99/1.63 c_Nat_OSuc, X ) ) ), Y = X }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), ! Y
% 0.99/1.63 = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.99/1.63 c_Nat_OSuc, X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.99/1.63 c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 0.99/1.63 , Y ) ), hAPP( c_Nat_OSuc, X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.99/1.63 c_Nat_OSuc, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Nat_Onat, Y ), X ) ), Y = X }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.99/1.63 c_Nat_OSuc, X ) ) ) }.
% 0.99/1.63 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 0.99/1.63 hAPP( c_Nat_OSuc, X ) ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP(
% 0.99/1.63 c_Nat_OSuc, Y ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP(
% 0.99/1.63 c_Nat_OSuc, Y ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.63 X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.99/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! X =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.63 X ), Z ) ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL(
% 0.99/1.63 hAPP( c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.63 X ), Z ) ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.63 X ), Z ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP(
% 0.99/1.63 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Z ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.63 X ), Y ) ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP(
% 0.99/1.63 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), hAPP(
% 0.99/1.63 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), hAPP(
% 0.99/1.63 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), hAPP(
% 0.99/1.63 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), hAPP(
% 0.99/1.63 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.63 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.63 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( X ), Z ), T ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, U ), T ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.63 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.63 ( X ), T ), Z ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y )
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.63 ( X ), Z ), T ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.63 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.63 ( c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.63 ( X ), T ), Z ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y )
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.63 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.63 ( c_Orderings_Oord__class_Oless( X, T ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.63 ( X ), T ), Z ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z )
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), T ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Y = Z, hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Z = Y, ! hBOOL( hAPP
% 0.99/1.63 ( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), Z = Y, ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), Z = Y, ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y, hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }
% 0.99/1.63 .
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), !
% 0.99/1.63 Y = X }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.99/1.63 , Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.63 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.63 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.63 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), T ) )
% 0.99/1.63 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, X ) ), hAPP
% 0.99/1.63 ( c_Int_Onat, Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Int_Oint, X ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, X ) ), hAPP
% 0.99/1.63 ( c_Int_Onat, Y ) ) ) }.
% 0.99/1.63 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 0.99/1.63 ( tc_fun( T, X ), Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ) }.
% 0.99/1.63 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 0.99/1.63 ( tc_fun( T, X ), Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y ), Z ) ) }.
% 0.99/1.63 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 0.99/1.63 hAPP( c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y ), Z ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z ), Y ) ) }
% 0.99/1.63 .
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, X ) ), hAPP
% 0.99/1.63 ( c_Int_Onat, Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Int_Oint, X ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, X ) ), hAPP
% 0.99/1.63 ( c_Int_Onat, Y ) ) ) }.
% 0.99/1.63 { ! class_Orderings_Owellorder( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), c_Orderings_Oord__class_OLeast( X
% 0.99/1.63 , Y ) ) ), ! hBOOL( hAPP( Y, Z ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), T ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) ) ) }.
% 0.99/1.63 { c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Int_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.99/1.63 { hAPP( c_Int_Onat, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hAPP( c_Int_Onat,
% 0.99/1.63 X ) = hAPP( c_Int_Onat, Y ), X = Y }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! X = Y, hAPP(
% 0.99/1.63 c_Int_Onat, X ) = hAPP( c_Int_Onat, Y ) }.
% 0.99/1.63 { ! hBOOL( hAPP( X, skol11( X ) ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( X, hAPP
% 0.99/1.63 ( c_Int_Onat, Y ) ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), skol32( Y ) ) ), hBOOL(
% 0.99/1.63 hAPP( X, Z ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( X, hAPP( c_Int_Onat, skol32( X ) ) ) ), hBOOL( hAPP( X, Y
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), skol12( Z ) )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, hAPP( c_Int_Onat, skol12( X ) )
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( X,
% 0.99/1.63 hAPP( c_Int_Onat, Y ) ) ), hBOOL( hAPP( X, skol33( X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hAPP( c_Int_Onat,
% 0.99/1.63 X ) = hAPP( c_Int_Onat, Y ), X = Y }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! X = Y, hAPP(
% 0.99/1.63 c_Int_Onat, X ) = hAPP( c_Int_Onat, Y ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), alpha8( X, Y, Z, T ),
% 0.99/1.63 alpha23( X, Y, Z, T ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha8( X, Y, Z, T ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha23( X, Y, Z, T ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.63 { ! alpha23( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z
% 0.99/1.63 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.63 { ! alpha23( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y
% 0.99/1.63 ), T ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), T ) ), alpha23( X, Y, Z, T ) }.
% 0.99/1.63 { ! alpha8( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 0.99/1.63 { ! alpha8( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T
% 0.99/1.63 ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, T ), Y ) ), alpha8( X, Y, Z, T ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), alpha9( X, Y, Z, T ),
% 0.99/1.63 alpha24( X, Y, Z, T ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( X, Y, Z, T ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha24( X, Y, Z, T ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.99/1.63 { ! alpha24( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T
% 0.99/1.63 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.63 { ! alpha24( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y
% 0.99/1.63 ), Z ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), alpha24( X, Y, Z, T ) }.
% 0.99/1.63 { ! alpha9( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), T ) ) }.
% 0.99/1.63 { ! alpha9( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z
% 0.99/1.63 ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), T ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), alpha9( X, Y, Z, T ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, T ), Z ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL(
% 0.99/1.63 hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), ! hBOOL(
% 0.99/1.63 hAPP( c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.63 ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), ! hBOOL(
% 0.99/1.63 hAPP( c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.63 ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), T ) ), hBOOL(
% 0.99/1.63 hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__comm__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, T ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, T ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) ) }.
% 0.99/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.63 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.63 ( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 0.99/1.63 ( X ) ) ) }.
% 0.99/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.63 ( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 0.99/1.63 ( X ) ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.63 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.63 ( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL(
% 0.99/1.63 hAPP( c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.63 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, U ), T ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.63 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.63 c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.63 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( c_Int_Onat,
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.63 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.63 ( X ), Y ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), hAPP(
% 0.99/1.63 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y ), hAPP(
% 0.99/1.63 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.63 X ), Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP(
% 0.99/1.63 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), c_Groups_Ozero__class_Ozero
% 0.99/1.63 ( X ) ) ) }.
% 0.99/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.63 X ), Y ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 0.99/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP(
% 0.99/1.63 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Y ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.63 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.63 c_Groups_Oone__class_Oone( X ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), hAPP
% 0.99/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.63 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP
% 0.99/1.63 ( c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.63 , ! T = Z, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP
% 0.99/1.63 ( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), X = hAPP( c_Nat_OSuc
% 0.99/1.63 , skol13( X ) ) }.
% 0.99/1.63 { ! X = hAPP( c_Nat_OSuc, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP(
% 0.99/1.63 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP( c_Nat_OSuc,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.99/1.63 c_Nat_OSuc, X ) ) ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.63 alpha10( X, Y ) }.
% 0.99/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( c_Nat_OSuc, X ) )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! alpha10( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Nat_Onat, Y ), hAPP( c_Nat_OSuc, X ) ) ) }.
% 0.99/1.63 { ! alpha10( X, Y ), Y = hAPP( c_Nat_OSuc, skol14( Z, Y ) ) }.
% 0.99/1.63 { ! alpha10( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Nat_Onat, skol14( X, Y ) ), X ) ) }.
% 0.99/1.63 { ! Y = hAPP( c_Nat_OSuc, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 0.99/1.63 ( tc_Nat_Onat, Z ), X ) ), alpha10( X, Y ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 0.99/1.63 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.99/1.63 Y ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.99/1.63 Y ), X ) ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.99/1.63 c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ),
% 0.99/1.63 X ) ) ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.99/1.63 c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 0.99/1.63 Y ) ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), X
% 0.99/1.63 = hAPP( c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.99/1.63 ), Y ), skol15( X, Y ) ) ) }.
% 0.99/1.63 { ! X = hAPP( c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.63 tc_Nat_Onat ), Y ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.63 c_Nat_OSuc, Y ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.63 c_Nat_OSuc, Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.99/1.63 c_Nat_OSuc, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.63 tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.99/1.63 c_Nat_OSuc, X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.63 c_Nat_OSuc, Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.63 c_Nat_OSuc, Y ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.99/1.63 c_Nat_OSuc, X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.63 c_Nat_OSuc, Y ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP(
% 0.99/1.63 c_Nat_OSuc, Y ) ) ), X = Y }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , ! X = Y, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 0.99/1.63 hAPP( c_Nat_OSuc, Y ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.63 c_Nat_OSuc, Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oone__class_Oone(
% 0.99/1.63 tc_Int_Oint ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Z = Y, hAPP( hAPP
% 0.99/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), Z ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), X ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), !
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), Y
% 0.99/1.63 ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 0.99/1.63 c_Nat_OSuc, Z ) ), X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), Y
% 0.99/1.63 ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 0.99/1.63 c_Nat_OSuc, Z ) ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), !
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ), Z ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Z ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP(
% 0.99/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), Y = X }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP( hAPP
% 0.99/1.63 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 0.99/1.63 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ),
% 0.99/1.63 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), Y ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.99/1.63 .
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.99/1.63 , Y ), X ) ) ) }.
% 0.99/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.99/1.63 , Y ), X ) ) ) }.
% 0.99/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ) =
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Nat_OSuc, X ) ) }
% 0.99/1.63 .
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hAPP( c_Int_Onat, X ) =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! hAPP( c_Int_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hAPP( c_Int_Onat, X ) =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { hAPP( c_Int_Onat, c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = hAPP(
% 0.99/1.63 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Int_Onat, X ) ),
% 0.99/1.63 hAPP( c_Int_Onat, Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.99/1.63 ( tc_Int_Oint, X ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Int_Onat, X ) ),
% 0.99/1.63 hAPP( c_Int_Onat, Y ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, U ), T ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, U ), T ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, U ), T ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Z )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 , Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 , Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Z )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.63 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.63 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Z ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.63 ( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.63 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.63 ( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.63 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP(
% 0.99/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.63 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ), ! Z =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.63 }.
% 0.99/1.63 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.63 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.63 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.63 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone(
% 0.99/1.63 X ) ), c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.63 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.63 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.63 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.63 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.63 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, Z ) ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.99/1.63 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), !
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 0.99/1.63 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.99/1.63 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), !
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 0.99/1.63 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.99/1.63 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), !
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc
% 0.99/1.63 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Int_Oint ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.99/1.63 ( tc_Int_Oint ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 0.99/1.63 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.63 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 0.99/1.63 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP
% 0.99/1.63 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.99/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), ! hBOOL( hAPP
% 0.99/1.63 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.63 ( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.99/1.63 tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), ! hBOOL( hAPP
% 0.99/1.63 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.63 ( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.99/1.63 ( tc_Nat_Onat, Z ), X ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), X ) )
% 0.99/1.63 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), ! hBOOL( hAPP
% 0.99/1.63 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.63 ( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.99/1.63 ( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.99/1.63 tc_Int_Oint ) ), X ) ), X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 0.99/1.63 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.99/1.63 tc_Int_Oint ) ), X ) ), X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ), X = c_Groups_Oone__class_Oone(
% 0.99/1.63 tc_Int_Oint ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y = c_Groups_Oone__class_Oone(
% 0.99/1.63 tc_Int_Oint ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! X =
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y = c_Groups_Oone__class_Oone
% 0.99/1.63 ( tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.99/1.63 , X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP(
% 0.99/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP(
% 0.99/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 0.99/1.63 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.99/1.63 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( c_Int_Onat, X ) ), hAPP
% 0.99/1.63 ( c_Int_Onat, Y ) ) = hAPP( c_Int_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hAPP( c_Int_Onat,
% 0.99/1.63 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) ) = hAPP
% 0.99/1.63 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( c_Int_Onat, X )
% 0.99/1.63 ), hAPP( c_Int_Onat, Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Int_Onat, X ) ),
% 0.99/1.63 hAPP( c_Int_Onat, Y ) ) = hAPP( c_Int_Onat, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP( c_Int_Onat,
% 0.99/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 0.99/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 0.99/1.63 c_Int_Onat, X ) ), hAPP( c_Int_Onat, Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( hAPP
% 0.99/1.63 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( c_Int_Onat, X ) ), hAPP
% 0.99/1.63 ( c_Int_Onat, Y ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.99/1.63 tc_Int_Oint ), X ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( hAPP
% 0.99/1.63 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), X ), Y ) ), hBOOL( hAPP( hAPP
% 0.99/1.63 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( c_Int_Onat, X ) ), hAPP
% 0.99/1.63 ( c_Int_Onat, Y ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y ),
% 0.99/1.63 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.63 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y ),
% 0.99/1.63 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, Z ) ) ),
% 0.99/1.63 c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.63 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.63 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.63 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 , T ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), Z ) ), T = Y }.
% 0.99/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X )
% 0.99/1.63 , Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.99/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), hAPP( c_Int_Onat, X ) ), Y )
% 0.99/1.63 = hAPP( c_Int_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.63 tc_Int_Oint ), X ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP( c_Int_Onat,
% 0.99/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) =
% 0.99/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), hAPP( c_Int_Onat
% 0.99/1.63 , X ) ), Y ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Int_Oint ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 0.99/1.63 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X ) ), Y =
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Y =
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.99/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP( hAPP
% 0.99/1.63 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ), X ) ), Y =
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Y =
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.99/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.99/1.63 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ) ), ! hBOOL( hAPP
% 0.99/1.63 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.99/1.63 tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.63 tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! X = hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z ), X ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.99/1.63 ( tc_Int_Oint ) ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! X = hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ) ), !
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Z ) ), !
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Int_Oint ) ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.63 tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.99/1.63 { alpha33( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Nat_Onat, Y ), Z ) ), hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.99/1.63 { alpha33( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.99/1.63 ( X, Y ), Z ) ) }.
% 0.99/1.63 { ! alpha33( X, Y, Z ), alpha34( X, Y, Z ), Z = Y }.
% 0.99/1.63 { ! alpha33( X, Y, Z ), alpha34( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! alpha34( X, Y, Z ), alpha33( X, Y, Z ) }.
% 0.99/1.63 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha33( X, Y, Z ) }.
% 0.99/1.63 { ! alpha34( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Nat_Onat, Z ), Y ) ) }.
% 0.99/1.63 { ! alpha34( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ),
% 0.99/1.63 hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha34( X, Y, Z ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.63 Y = X }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.63 X = Y }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), X ) ) }.
% 0.99/1.63 { Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ) }
% 0.99/1.63 .
% 0.99/1.63 { Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ) }
% 0.99/1.63 .
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.63 Y = X }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ), !
% 0.99/1.63 Y = X }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), X ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), Y =
% 0.99/1.63 X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ) }
% 0.99/1.63 .
% 0.99/1.63 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ) ), T ) = hAPP(
% 0.99/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), ! hBOOL(
% 0.99/1.63 hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, T ), W ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.99/1.63 ( tc_Int_Oint, Z ), W ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.99/1.63 ( tc_Int_Oint, Y ), U ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 0.99/1.63 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ) ), Z ) ), hAPP(
% 0.99/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ) ), X ) ) ), !
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, U ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, U ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), T ) ) }.
% 0.99/1.63 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ) ), T ) = hAPP(
% 0.99/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), ! hBOOL(
% 0.99/1.63 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ) ), !
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Z ) ), !
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.99/1.63 ( tc_Int_Oint, Z ), W ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.99/1.63 ( tc_Int_Oint, U ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 0.99/1.63 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ) ), Z ) ), hAPP(
% 0.99/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ) ), X ) ) ), !
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z ), U ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), U ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ), Y ) ) }.
% 0.99/1.63 { c_Int_Onat__aux( Y, X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.63 tc_Nat_Onat ), hAPP( c_Int_Onat, Y ) ), X ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), X =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), Y ) ) }.
% 0.99/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.99/1.63 , Y ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.99/1.63 , Y ), X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP(
% 0.99/1.63 c_Nat_OSuc, hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.63 ) ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = hAPP(
% 0.99/1.63 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.63 { c_Nat__Transfer_Otransfer__morphism( tc_Int_Oint, tc_Nat_Onat, c_Int_Onat
% 0.99/1.63 , c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Ostrict__mono(
% 0.99/1.63 tc_Nat_Onat, X, hAPP( hAPP( c_COMBS( tc_Nat_Onat, tc_fun( tc_Nat_Onat,
% 0.99/1.63 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ) ), hAPP( hAPP(
% 0.99/1.63 c_COMBB( tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ),
% 0.99/1.63 tc_fun( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat,
% 0.99/1.63 tc_HOL_Obool ) ), tc_Nat_Onat ), c_COMBS( tc_Nat_Onat, tc_HOL_Obool,
% 0.99/1.63 tc_HOL_Obool ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool
% 0.99/1.63 ), tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ),
% 0.99/1.63 tc_Nat_Onat ), hAPP( c_COMBB( tc_HOL_Obool, tc_fun( tc_HOL_Obool,
% 0.99/1.63 tc_HOL_Obool ), tc_Nat_Onat ), c_fconj ) ), c_Rings_Odvd__class_Odvd(
% 0.99/1.63 tc_Nat_Onat ) ) ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat,
% 0.99/1.63 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_Nat_Onat ), hAPP
% 0.99/1.63 ( c_COMBB( tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat ), c_fNot ) ), c_COMBC
% 0.99/1.63 ( tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool, c_Rings_Odvd__class_Odvd(
% 0.99/1.63 tc_Nat_Onat ) ) ) ), Y ), c_Orderings_Oorder_Omono( tc_Nat_Onat, X,
% 0.99/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ) }.
% 0.99/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Ostrict__mono(
% 0.99/1.63 tc_Nat_Onat, X, hAPP( hAPP( c_COMBS( tc_Nat_Onat, tc_fun( tc_Nat_Onat,
% 0.99/1.63 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ) ), hAPP( hAPP(
% 0.99/1.63 c_COMBB( tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ),
% 0.99/1.63 tc_fun( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat,
% 0.99/1.63 tc_HOL_Obool ) ), tc_Nat_Onat ), c_COMBS( tc_Nat_Onat, tc_HOL_Obool,
% 0.99/1.63 tc_HOL_Obool ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool
% 0.99/1.63 ), tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ),
% 0.99/1.63 tc_Nat_Onat ), hAPP( c_COMBB( tc_HOL_Obool, tc_fun( tc_HOL_Obool,
% 0.99/1.63 tc_HOL_Obool ), tc_Nat_Onat ), c_fconj ) ), c_Rings_Odvd__class_Odvd(
% 0.99/1.63 tc_Nat_Onat ) ) ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat,
% 0.99/1.63 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_Nat_Onat ), hAPP
% 0.99/1.63 ( c_COMBB( tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat ), c_fNot ) ), c_COMBC
% 0.99/1.63 ( tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool, c_Rings_Odvd__class_Odvd(
% 0.99/1.63 tc_Nat_Onat ) ) ) ), Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.99/1.63 tc_Nat_Onat ), T ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.99/1.63 tc_Nat_Onat ), Z ), T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X
% 0.99/1.63 , hAPP( Y, T ) ), hAPP( Y, Z ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, hAPP
% 0.99/1.63 ( hAPP( c_Polynomial_OpCons( X ), Z ), Y ) ), c_Polynomial_Opos__poly( X
% 0.99/1.63 , Y ), alpha11( X, Y, Z ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.99/1.63 c_Polynomial_Opos__poly( X, hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), ! alpha11( X, Y, Z ),
% 0.99/1.63 c_Polynomial_Opos__poly( X, hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y
% 0.99/1.63 ) ) }.
% 0.99/1.63 { ! alpha11( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.63 { ! alpha11( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 0.99/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! hBOOL(
% 0.99/1.63 hAPP( c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.63 ), Z ) ), alpha11( X, Y, Z ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP( Y,
% 0.99/1.63 skol16( Z, Y ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! hBOOL
% 0.99/1.63 ( hAPP( Y, U ) ), hBOOL( hAPP( Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.63 ( tc_Int_Oint ), U ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.63 tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( Y,
% 0.99/1.63 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), skol16( X, Y ) )
% 0.99/1.63 , X ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint
% 0.99/1.63 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP( Y,
% 0.99/1.63 T ) ), hBOOL( hAPP( Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.63 tc_Int_Oint ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.63 tc_Int_Oint ), Z ), X ) ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.99/1.63 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.99/1.63 ( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.99/1.63 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.99/1.63 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.99/1.63 .
% 0.99/1.63 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.99/1.63 c_Polynomial_Opos__poly( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.63 tc_Polynomial_Opoly( X ) ), Y ) ) }.
% 0.99/1.63 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.99/1.63 hAPP( X, Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 skol17( Z, Y ) ), Y ) ) }.
% 0.99/1.63 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.99/1.63 hAPP( X, Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.63 tc_Nat_Onat, Z ), skol17( X, Y ) ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.99/1.63 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.99/1.63 hAPP( X, Y ) ), hBOOL( hAPP( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.63 tc_Nat_Onat ), skol17( X, Y ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 0.99/1.63 ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP(
% 0.99/1.63 c_Int_Onat, Y ) ), X ) ), alpha12( X, Y ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP(
% 0.99/1.63 c_Int_Onat, Y ) ), X ) ), alpha25( X, Y ) }.
% 0.99/1.63 { ! alpha12( X, Y ), ! alpha25( X, Y ), hBOOL( hAPP( hAPP(
% 0.99/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( c_Int_Onat, Y ) ), X ) ) }
% 0.99/1.63 .
% 0.99/1.63 { ! alpha25( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), X =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), alpha25( X, Y ) }.
% 0.99/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha25( X, Y ) }.
% 0.99/1.63 { ! alpha12( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL(
% 0.99/1.63 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), alpha12( X, Y ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ), alpha12( X, Y )
% 0.99/1.63 }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.99/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.99/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( c_Nat_OSuc, Y ) )
% 0.99/1.63 ) ), c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) }.
% 0.99/1.63 { hAPP( c_Int_Onat, c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) )
% 0.99/1.63 = X }.
% 0.99/1.63 { ! c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) =
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ), Y = X }.
% 0.99/1.63 { ! Y = X, c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) =
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) }.
% 0.99/1.63 { ! c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) =
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ), Y = X }.
% 0.99/1.63 { ! Y = X, c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) =
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) }.
% 0.99/1.63 { ! class_Nat_Osemiring__char__0( X ), ! c_Nat_Osemiring__1__class_Oof__nat
% 0.99/1.63 ( X, Z ) = c_Nat_Osemiring__1__class_Oof__nat( X, Y ), Z = Y }.
% 0.99/1.63 { ! class_Nat_Osemiring__char__0( X ), ! Z = Y,
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( X, Z ) =
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( X, Y ) }.
% 0.99/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ), X ) =
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.63 { c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ), X ) }.
% 0.99/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ), X ) =
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ), hBOOL( hAPP(
% 0.99/1.63 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ), hBOOL( hAPP(
% 0.99/1.63 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.63 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat( X,
% 0.99/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ) =
% 0.99/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( X, Z ) ), Y ) }.
% 0.99/1.63 { c_Groups_Oone__class_Oone( tc_Int_Oint ) =
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.99/1.63 { c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone(
% 0.99/1.63 tc_Int_Oint ) }.
% 0.99/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) =
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.63 { c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) }.
% 0.99/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) =
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.63 { ! hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ) =
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ), Y =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ) =
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ), X =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP(
% 0.99/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ) =
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) }.
% 0.99/1.63 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) =
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.63 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) =
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.63 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Z ) ), hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ), X ) ) = hAPP(
% 0.99/1.63 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) ), X ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.99/1.63 , X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, skol18( X, Y ) ) ) }.
% 0.99/1.63 { ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.63 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), skol19( Y ) ) ), hBOOL(
% 0.99/1.63 hAPP( X, c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Z ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( X, skol19( X ) ) ), hBOOL( hAPP( X,
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( X, c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, skol34
% 0.99/1.63 ( X ) ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL(
% 0.99/1.63 hAPP( X, Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( X, Y
% 0.99/1.63 ) ), hBOOL( hAPP( X, c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 0.99/1.63 skol20( X ) ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( X, c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), skol35( Z ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( X, c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) )
% 0.99/1.63 ), hBOOL( hAPP( X, skol35( X ) ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) }.
% 0.99/1.63 { c_Groups_Ozero__class_Ozero( tc_Int_Oint ) =
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.63 { ! c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.63 { c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.63 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat( X,
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X
% 0.99/1.63 ) }.
% 0.99/1.63 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat( X,
% 0.99/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) =
% 0.99/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( X, Z ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) }.
% 0.99/1.63 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat( X,
% 0.99/1.63 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) = hAPP
% 0.99/1.63 ( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( X, Z ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Nat_Osemiring__1__class_Oof__nat
% 0.99/1.63 ( X, Z ) ), c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Nat_Osemiring__1__class_Oof__nat
% 0.99/1.63 ( X, Z ) ), c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) ) }.
% 0.99/1.63 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Nat_Osemiring__1__class_Oof__nat( X,
% 0.99/1.63 Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 , c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.63 , c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ), hAPP(
% 0.99/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Nat_Osemiring__1__class_Oof__nat( X,
% 0.99/1.63 Z ) ), c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Nat_Osemiring__1__class_Oof__nat( X,
% 0.99/1.63 Z ) ), c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Nat_Osemiring__1__class_Oof__nat( X,
% 0.99/1.63 Z ) ), c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Nat_Osemiring__1__class_Oof__nat( X,
% 0.99/1.63 Z ) ), c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.99/1.63 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat( X,
% 0.99/1.63 hAPP( c_Nat_OSuc, Y ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 0.99/1.63 c_Groups_Oone__class_Oone( X ) ), c_Nat_Osemiring__1__class_Oof__nat( X,
% 0.99/1.63 Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), X =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.99/1.63 { c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( c_Nat_OSuc,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), X
% 0.99/1.63 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( c_Nat_OSuc, skol21
% 0.99/1.63 ( X, Y ) ) ) ) }.
% 0.99/1.63 { ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( c_Nat_OSuc, Z ) )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ) }
% 0.99/1.63 .
% 0.99/1.63 { c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( c_Nat_OSuc, X ) )
% 0.99/1.63 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 0.99/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( c_Int_Onat, X ) )
% 0.99/1.63 = X }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( c_Int_Onat, X ) )
% 0.99/1.63 = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.63 { ! c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) = X, Y = hAPP(
% 0.99/1.63 c_Int_Onat, X ) }.
% 0.99/1.63 { ! c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) = X, hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ) }.
% 0.99/1.63 { ! Y = hAPP( c_Int_Onat, X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) = X }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( c_Int_Onat, X ) )
% 0.99/1.63 = X }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ), hAPP(
% 0.99/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) ), Y =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ), hAPP(
% 0.99/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) ), X =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ), hAPP(
% 0.99/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 0.99/1.63 c_Int_Onat, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ), X )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ), X ) ), hBOOL(
% 0.99/1.63 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( c_Int_Onat,
% 0.99/1.63 X ) ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.99/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.99/1.63 { hAPP( c_Int_Onat, hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), Y ) ) }.
% 0.99/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Nat_Osemiring__1__class_Oof__nat( X
% 0.99/1.63 , Y ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Int_Oint ) ), c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) )
% 0.99/1.63 }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), !
% 0.99/1.63 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Z ) ), Y ) ), hAPP( hAPP
% 0.99/1.63 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Z ) ), X ) ) ) }.
% 0.99/1.63 { ! Y = hAPP( c_Int_Onat, X ), alpha13( X, Y ) }.
% 0.99/1.63 { ! Y = hAPP( c_Int_Onat, X ), alpha26( X, Y ) }.
% 0.99/1.63 { ! alpha13( X, Y ), ! alpha26( X, Y ), Y = hAPP( c_Int_Onat, X ) }.
% 0.99/1.63 { ! alpha26( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), Y =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha26( X, Y ) }.
% 0.99/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha26( X, Y ) }.
% 0.99/1.63 { ! alpha13( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), X =
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha13( X, Y ) }.
% 0.99/1.63 { ! X = c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ), alpha13( X, Y
% 0.99/1.63 ) }.
% 0.99/1.63 { ! hAPP( c_Int_Onat, Y ) = X, alpha14( X, Y ) }.
% 0.99/1.63 { ! hAPP( c_Int_Onat, Y ) = X, alpha27( X, Y ) }.
% 0.99/1.63 { ! alpha14( X, Y ), ! alpha27( X, Y ), hAPP( c_Int_Onat, Y ) = X }.
% 0.99/1.63 { ! alpha27( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), X =
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), alpha27( X, Y ) }.
% 0.99/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha27( X, Y ) }.
% 0.99/1.63 { ! alpha14( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.63 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), Y =
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), alpha14( X, Y ) }.
% 0.99/1.63 { ! Y = c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ), alpha14( X, Y
% 0.99/1.63 ) }.
% 0.99/1.63 { ! hBOOL( hAPP( Y, hAPP( c_Int_Onat, X ) ) ), alpha15( X, Y ) }.
% 0.99/1.63 { ! hBOOL( hAPP( Y, hAPP( c_Int_Onat, X ) ) ), alpha28( X, Y ) }.
% 0.99/1.63 { ! alpha15( X, Y ), ! alpha28( X, Y ), hBOOL( hAPP( Y, hAPP( c_Int_Onat, X
% 0.99/1.63 ) ) ) }.
% 0.99/1.63 { ! alpha28( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Int_Oint, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL(
% 0.99/1.63 hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha28( X, Y ) }.
% 0.99/1.63 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha28
% 0.99/1.63 ( X, Y ) }.
% 0.99/1.63 { ! alpha15( X, Y ), ! X = c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint
% 0.99/1.63 , Z ), hBOOL( hAPP( Y, Z ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( Y, skol22( Z, Y ) ) ), alpha15( X, Y ) }.
% 0.99/1.63 { X = c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, skol22( X, Y ) ),
% 0.99/1.63 alpha15( X, Y ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP(
% 0.99/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( c_Nat_OSuc, X ) )
% 0.99/1.63 ) ) ) }.
% 0.99/1.63 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.99/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( c_Nat_OSuc, X ) )
% 0.99/1.63 ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, X ) ), Y )
% 0.99/1.63 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, X ) ), Y )
% 0.99/1.63 ) }.
% 0.99/1.63 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat( X, Y
% 0.99/1.63 ) = c_Nat_Osemiring__1__class_Oof__nat__aux( X, hAPP( c_COMBC( X, X, X,
% 0.99/1.63 c_Groups_Oplus__class_Oplus( X ) ), c_Groups_Oone__class_Oone( X ) ), Y,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), X = hAPP(
% 0.99/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( c_Nat_OSuc, skol23
% 0.99/1.63 ( X ) ) ) ) }.
% 0.99/1.63 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat__aux
% 0.99/1.63 ( X, Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) = Y }.
% 0.99/1.63 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat__aux
% 0.99/1.63 ( X, T, hAPP( c_Nat_OSuc, Z ), Y ) =
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat__aux( X, T, Z, hAPP( T, Y ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 0.99/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.63 tc_Nat_Onat ) ), skol24( Y ) ) ) }.
% 0.99/1.63 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), X =
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, skol24( X ) ) }.
% 0.99/1.63 { ! class_Rings_Oring__1( X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 0.99/1.63 ( tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ),
% 0.99/1.63 c_Int_Oring__1__class_Oof__int( X, Y ) = hAPP(
% 0.99/1.63 c_Groups_Ouminus__class_Ouminus( X ), c_Nat_Osemiring__1__class_Oof__nat
% 0.99/1.63 ( X, hAPP( c_Int_Onat, hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint
% 0.99/1.63 ), Y ) ) ) ) }.
% 0.99/1.63 { ! class_Rings_Oring__1( X ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.63 tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ),
% 0.99/1.63 c_Int_Oring__1__class_Oof__int( X, Y ) =
% 0.99/1.63 c_Nat_Osemiring__1__class_Oof__nat( X, hAPP( c_Int_Onat, Y ) ) }.
% 0.99/1.64 { ! class_Rings_Oring__1( X ), c_Int_Oring__1__class_Oof__int( X,
% 0.99/1.64 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ) =
% 0.99/1.64 c_Nat_Osemiring__1__class_Oof__nat( X, Y ) }.
% 0.99/1.64 { c_Int_Oring__1__class_Oof__int( tc_Int_Oint,
% 0.99/1.64 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) =
% 0.99/1.64 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) }.
% 0.99/1.64 { ! class_Int_Oring__char__0( X ), ! c_Int_Oring__1__class_Oof__int( X, Z )
% 0.99/1.64 = c_Int_Oring__1__class_Oof__int( X, Y ), Z = Y }.
% 0.99/1.64 { ! class_Int_Oring__char__0( X ), ! Z = Y, c_Int_Oring__1__class_Oof__int
% 0.99/1.64 ( X, Z ) = c_Int_Oring__1__class_Oof__int( X, Y ) }.
% 0.99/1.64 { ! class_Rings_Oring__1( X ), c_Int_Oring__1__class_Oof__int( X, hAPP(
% 0.99/1.64 hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ) = hAPP(
% 0.99/1.64 hAPP( c_Power_Opower__class_Opower( X ), c_Int_Oring__1__class_Oof__int(
% 0.99/1.64 X, Z ) ), Y ) }.
% 0.99/1.64 { ! class_Rings_Oring__1( X ), c_Int_Oring__1__class_Oof__int( X, hAPP(
% 0.99/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ) = hAPP(
% 0.99/1.64 c_Groups_Ouminus__class_Ouminus( X ), c_Int_Oring__1__class_Oof__int( X,
% 0.99/1.64 Y ) ) }.
% 0.99/1.64 { ! class_Rings_Oring__1( X ), c_Int_Oring__1__class_Oof__int( X,
% 0.99/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = c_Groups_Oone__class_Oone( X
% 0.99/1.64 ) }.
% 0.99/1.64 { ! class_Rings_Oring__1( X ), c_Int_Oring__1__class_Oof__int( X, hAPP(
% 0.99/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) = hAPP(
% 0.99/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Int_Oring__1__class_Oof__int
% 0.99/1.64 ( X, Z ) ), c_Int_Oring__1__class_Oof__int( X, Y ) ) }.
% 0.99/1.64 { ! class_Rings_Oring__1( X ), c_Int_Oring__1__class_Oof__int( X, hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ) = hAPP( hAPP
% 0.99/1.64 ( c_Groups_Oplus__class_Oplus( X ), c_Int_Oring__1__class_Oof__int( X, Z
% 0.99/1.64 ) ), c_Int_Oring__1__class_Oof__int( X, Y ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Int_Oring__1__class_Oof__int( X,
% 0.99/1.64 Z ) ), c_Int_Oring__1__class_Oof__int( X, Y ) ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z ), Y ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Int_Oring__1__class_Oof__int( X,
% 0.99/1.64 Z ) ), c_Int_Oring__1__class_Oof__int( X, Y ) ) ) }.
% 0.99/1.64 { ! class_Rings_Oring__1( X ), c_Int_Oring__1__class_Oof__int( X,
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) =
% 0.99/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.64 { ! class_Int_Oring__char__0( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.99/1.64 c_Int_Oring__1__class_Oof__int( X, Y ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.64 tc_Int_Oint ) }.
% 0.99/1.64 { ! class_Int_Oring__char__0( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.64 tc_Int_Oint ), c_Groups_Ozero__class_Ozero( X ) =
% 0.99/1.64 c_Int_Oring__1__class_Oof__int( X, Y ) }.
% 0.99/1.64 { ! class_Int_Oring__char__0( X ), ! c_Int_Oring__1__class_Oof__int( X, Y )
% 0.99/1.64 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.64 tc_Int_Oint ) }.
% 0.99/1.64 { ! class_Int_Oring__char__0( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.64 tc_Int_Oint ), c_Int_Oring__1__class_Oof__int( X, Y ) =
% 0.99/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( X, c_Int_Oring__1__class_Oof__int( X, Z )
% 0.99/1.64 ), c_Int_Oring__1__class_Oof__int( X, Y ) ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z ), Y ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( X, c_Int_Oring__1__class_Oof__int( X, Z )
% 0.99/1.64 ), c_Int_Oring__1__class_Oof__int( X, Y ) ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.64 , c_Int_Oring__1__class_Oof__int( X, Y ) ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.64 , c_Int_Oring__1__class_Oof__int( X, Y ) ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Int_Oring__1__class_Oof__int( X,
% 0.99/1.64 Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Int_Oring__1__class_Oof__int( X,
% 0.99/1.64 Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( X, c_Int_Oring__1__class_Oof__int( X, Y )
% 0.99/1.64 ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ),
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ),
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( X, c_Int_Oring__1__class_Oof__int( X, Y )
% 0.99/1.64 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.64 c_Int_Oring__1__class_Oof__int( X, Y ) ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.64 tc_Int_Oint ) ), Y ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.64 tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Int_Oring__1__class_Oof__int( X, Y
% 0.99/1.64 ) ) ) }.
% 0.99/1.64 { ! class_Rings_Oring__1( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ),
% 0.99/1.64 c_Nat_Osemiring__1__class_Oof__nat( X, hAPP( c_Int_Onat, Y ) ) =
% 0.99/1.64 c_Int_Oring__1__class_Oof__int( X, Y ) }.
% 0.99/1.64 { ! class_Orderings_Oorder( X ), hBOOL( hAPP( hAPP(
% 0.99/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), skol25( X, Y ) ), skol36( X, Y )
% 0.99/1.64 ) ), c_Orderings_Oorder_Ostrict__mono( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.64 c_COMBS( tc_Nat_Onat, tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun(
% 0.99/1.64 tc_Nat_Onat, tc_HOL_Obool ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat,
% 0.99/1.64 tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ), tc_fun( tc_fun( tc_Nat_Onat,
% 0.99/1.64 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ) ), tc_Nat_Onat ),
% 0.99/1.64 c_COMBS( tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool ) ), hAPP( hAPP( c_COMBB
% 0.99/1.64 ( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_fun(
% 0.99/1.64 tc_HOL_Obool, tc_HOL_Obool ) ), tc_Nat_Onat ), hAPP( c_COMBB(
% 0.99/1.64 tc_HOL_Obool, tc_fun( tc_HOL_Obool, tc_HOL_Obool ), tc_Nat_Onat ),
% 0.99/1.64 c_fconj ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.99/1.64 c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat,
% 0.99/1.64 tc_HOL_Obool ), tc_Nat_Onat ), hAPP( c_COMBB( tc_HOL_Obool, tc_HOL_Obool
% 0.99/1.64 , tc_Nat_Onat ), c_fNot ) ), c_COMBC( tc_Nat_Onat, tc_Nat_Onat,
% 0.99/1.64 tc_HOL_Obool, c_Rings_Odvd__class_Odvd( tc_Nat_Onat ) ) ) ), Y ) }.
% 0.99/1.64 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP( hAPP(
% 0.99/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), skol36( X, Y ) ), skol25( X, Y )
% 0.99/1.64 ) ), c_Orderings_Oorder_Ostrict__mono( tc_Nat_Onat, X, hAPP( hAPP(
% 0.99/1.64 c_COMBS( tc_Nat_Onat, tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun(
% 0.99/1.64 tc_Nat_Onat, tc_HOL_Obool ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat,
% 0.99/1.64 tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ), tc_fun( tc_fun( tc_Nat_Onat,
% 0.99/1.64 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ) ), tc_Nat_Onat ),
% 0.99/1.64 c_COMBS( tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool ) ), hAPP( hAPP( c_COMBB
% 0.99/1.64 ( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_fun(
% 0.99/1.64 tc_HOL_Obool, tc_HOL_Obool ) ), tc_Nat_Onat ), hAPP( c_COMBB(
% 0.99/1.64 tc_HOL_Obool, tc_fun( tc_HOL_Obool, tc_HOL_Obool ), tc_Nat_Onat ),
% 0.99/1.64 c_fconj ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.99/1.64 c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat,
% 0.99/1.64 tc_HOL_Obool ), tc_Nat_Onat ), hAPP( c_COMBB( tc_HOL_Obool, tc_HOL_Obool
% 0.99/1.64 , tc_Nat_Onat ), c_fNot ) ), c_COMBC( tc_Nat_Onat, tc_Nat_Onat,
% 0.99/1.64 tc_HOL_Obool, c_Rings_Odvd__class_Odvd( tc_Nat_Onat ) ) ) ), Y ) }.
% 0.99/1.64 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( X, hAPP( Y, skol25( X, Y ) ) ), hAPP( Y,
% 0.99/1.64 skol36( X, Y ) ) ) ), c_Orderings_Oorder_Ostrict__mono( tc_Nat_Onat, X,
% 0.99/1.64 hAPP( hAPP( c_COMBS( tc_Nat_Onat, tc_fun( tc_Nat_Onat, tc_HOL_Obool ),
% 0.99/1.64 tc_fun( tc_Nat_Onat, tc_HOL_Obool ) ), hAPP( hAPP( c_COMBB( tc_fun(
% 0.99/1.64 tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ), tc_fun( tc_fun(
% 0.99/1.64 tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ) ),
% 0.99/1.64 tc_Nat_Onat ), c_COMBS( tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool ) ), hAPP
% 0.99/1.64 ( hAPP( c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat
% 0.99/1.64 , tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ), tc_Nat_Onat ), hAPP( c_COMBB(
% 0.99/1.64 tc_HOL_Obool, tc_fun( tc_HOL_Obool, tc_HOL_Obool ), tc_Nat_Onat ),
% 0.99/1.64 c_fconj ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.99/1.64 c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat,
% 0.99/1.64 tc_HOL_Obool ), tc_Nat_Onat ), hAPP( c_COMBB( tc_HOL_Obool, tc_HOL_Obool
% 0.99/1.64 , tc_Nat_Onat ), c_fNot ) ), c_COMBC( tc_Nat_Onat, tc_Nat_Onat,
% 0.99/1.64 tc_HOL_Obool, c_Rings_Odvd__class_Odvd( tc_Nat_Onat ) ) ) ), Y ) }.
% 0.99/1.64 { ! class_Groups_Omonoid__mult( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.64 tc_Nat_Onat ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ),
% 0.99/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) = hAPP( hAPP(
% 0.99/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.99/1.64 { ! class_Rings_Oring__1( X ), c_Int_Oring__1__class_Oof__int( X, hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Z ), Y ) ) = hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( X ), c_Int_Oring__1__class_Oof__int
% 0.99/1.64 ( X, Z ) ), c_Int_Oring__1__class_Oof__int( X, Y ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), Z ) ),
% 0.99/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), Z ) ), X ) ) }.
% 0.99/1.64 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ), hAPP(
% 0.99/1.64 c_Nat_OSuc, Y ) ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.64 tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.64 tc_Nat_Onat, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y
% 0.99/1.64 ), X ) ), Y ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ),
% 0.99/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.99/1.64 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), hAPP
% 0.99/1.64 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) = Y }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ), hBOOL(
% 0.99/1.64 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ), Y ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ), Y ) ), hBOOL(
% 0.99/1.64 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.99/1.64 { ! class_Groups_Oordered__ab__group__add( X ), ! hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( X, U ), T ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.64 { ! class_Groups_Oordered__ab__group__add( X ), ! hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( X, U ), T ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ),
% 0.99/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.99/1.64 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.64 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Z ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.99/1.64 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Z ) )
% 0.99/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) ) }.
% 0.99/1.64 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ),
% 0.99/1.64 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.64 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ),
% 0.99/1.64 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.64 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ),
% 0.99/1.64 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.64 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ),
% 0.99/1.64 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.64 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( X )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP
% 0.99/1.64 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), T ), Y ) ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), Y ) ) }.
% 0.99/1.64 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP
% 0.99/1.64 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ) = Y }.
% 0.99/1.64 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ) = Y, hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) }.
% 0.99/1.64 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP
% 0.99/1.64 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ), T = hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) }.
% 0.99/1.64 { ! class_Rings_Oring( X ), ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.64 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) }.
% 0.99/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.64 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), T ), Y ) ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), Y ) ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), T ), Y ) ) ) }.
% 0.99/1.64 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.64 ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.99/1.64 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP(
% 0.99/1.64 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.99/1.64 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP(
% 0.99/1.64 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.99/1.64 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), hAPP(
% 0.99/1.64 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__ring__1( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP(
% 0.99/1.64 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.99/1.64 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.99/1.64 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) =
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.64 { ! hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP(
% 0.99/1.64 c_Nat_OSuc, X ) ), Y ) = hAPP( c_Nat_OSuc, hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ), ! hBOOL
% 0.99/1.64 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ), !
% 0.99/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ),
% 0.99/1.64 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }
% 0.99/1.64 .
% 0.99/1.64 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ), ! hBOOL
% 0.99/1.64 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), !
% 0.99/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ),
% 0.99/1.64 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }
% 0.99/1.64 .
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ), Y ) = hAPP( hAPP
% 0.99/1.64 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), Z ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), Z ) = hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ), Y ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ), Y ) = hAPP( hAPP
% 0.99/1.64 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) =
% 0.99/1.64 Z, X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) }
% 0.99/1.64 .
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) = Z
% 0.99/1.64 }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), Y ) = X }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 0.99/1.64 hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) ),
% 0.99/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ),
% 0.99/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP
% 0.99/1.64 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ), Y ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.99/1.64 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) = X }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), hAPP
% 0.99/1.64 ( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ), Y ) ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.64 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL
% 0.99/1.64 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), hAPP
% 0.99/1.64 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ), hBOOL(
% 0.99/1.64 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) = hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) }.
% 0.99/1.64 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP(
% 0.99/1.64 c_Nat_OSuc, X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.99/1.64 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), hAPP(
% 0.99/1.64 c_Nat_OSuc, X ) ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus(
% 0.99/1.64 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ),
% 0.99/1.64 Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) }.
% 0.99/1.64 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), X ) ), Y ) }.
% 0.99/1.64 { ! class_Groups_Ominus( X ), hAPP( hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_fun( U, X ) ), T ), Z ), Y ) = hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP( T, Y ) ), hAPP( Z, Y ) )
% 0.99/1.64 }.
% 0.99/1.64 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), T ), Z )
% 0.99/1.64 ), Y ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP(
% 0.99/1.64 c_Polynomial_Ocoeff( X, T ), Y ) ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 0.99/1.64 ) ) }.
% 0.99/1.64 { ! class_Groups_Ominus( X ), hAPP( hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_fun( U, X ) ), T ), Z ), Y ) = hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP( T, Y ) ), hAPP( Z, Y ) )
% 0.99/1.64 }.
% 0.99/1.64 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ),
% 0.99/1.64 c_Polynomial_Omonom( X, T, Z ) ), c_Polynomial_Omonom( X, Y, Z ) ) =
% 0.99/1.64 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), T
% 0.99/1.64 ), Y ), Z ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X, hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), T ), Z ) ), Y
% 0.99/1.64 ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP(
% 0.99/1.64 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.99/1.64 ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__ring( X ), hAPP( hAPP( c_Polynomial_Osmult( X ),
% 0.99/1.64 hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) = hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), hAPP(
% 0.99/1.64 hAPP( c_Polynomial_Osmult( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.64 c_Polynomial_Osmult( X ), Z ), Y ) ) }.
% 0.99/1.64 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 0.99/1.64 c_Polynomial_OpCons( X ), U ), T ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 0.99/1.64 ), Z ), Y ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 0.99/1.64 { ! class_Groups_Oab__group__add( X ), ! hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), ! U = T, Z = Y }.
% 0.99/1.64 { ! class_Groups_Oab__group__add( X ), ! hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), ! Z = Y, U = T }.
% 0.99/1.64 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), Z ), Y ) =
% 0.99/1.64 c_Polynomial_OAbs__poly( X, hAPP( hAPP( c_COMBS( tc_Nat_Onat, X, X ),
% 0.99/1.64 hAPP( hAPP( c_COMBB( X, tc_fun( X, X ), tc_Nat_Onat ),
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ) ), c_Polynomial_Ocoeff( X, Z ) ) ),
% 0.99/1.64 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 0.99/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP
% 0.99/1.64 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.99/1.64 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) ), hBOOL(
% 0.99/1.64 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.99/1.64 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z
% 0.99/1.64 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.99/1.64 ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP
% 0.99/1.64 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Z ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.99/1.64 ), ! hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y )
% 0.99/1.64 = hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ), X =
% 0.99/1.64 Z }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.99/1.64 ), ! X = Z, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X
% 0.99/1.64 ), Y ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ),
% 0.99/1.64 Y ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) = Y }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.64 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.64 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) ) }.
% 0.99/1.64 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ), Y ) ) }.
% 0.99/1.64 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), X ) }.
% 0.99/1.64 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) }.
% 0.99/1.64 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.64 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), Y ) = X }.
% 0.99/1.64 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), X ) = Y }.
% 0.99/1.64 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), Y
% 0.99/1.64 ) ), hAPP( c_Nat_OSuc, X ) ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 0.99/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat )
% 0.99/1.64 , Z ), Y ) ), X ) }.
% 0.99/1.64 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP(
% 0.99/1.64 c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) }.
% 0.99/1.64 { ! hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) =
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.99/1.64 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), X ) =
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.64 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ),
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.99/1.64 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ),
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.99/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.99/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.99/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Y ), T ) ) ) }.
% 0.99/1.64 { ! class_Groups_Oab__group__add( X ), hAPP(
% 0.99/1.64 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Y ), Z ) }.
% 0.99/1.64 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ), Y ) = Z }.
% 0.99/1.64 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.64 ( X ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ), Y ) =
% 0.99/1.64 Z }.
% 0.99/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.64 { ! class_Groups_Oordered__ab__group__add( X ), ! hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.64 { ! class_Groups_Oordered__ab__group__add( X ), ! hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ) }.
% 0.99/1.64 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) =
% 0.99/1.64 c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.99/1.64 { ! class_Groups_Ogroup__add( X ), ! Z = Y, hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) =
% 0.99/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.64 { ! class_Groups_Oab__group__add( X ), ! Z = Y, hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) =
% 0.99/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.64 { ! class_Groups_Oab__group__add( X ), ! hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) =
% 0.99/1.64 c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.99/1.64 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Y ), Y ) =
% 0.99/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.64 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.99/1.64 ) = Y }.
% 0.99/1.64 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.99/1.64 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.99/1.64 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), hAPP
% 0.99/1.64 ( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.64 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), hAPP(
% 0.99/1.64 c_Nat_OSuc, X ) ) = hAPP( c_Nat_Onat_Onat__case( tc_Nat_Onat,
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_COMBI( tc_Nat_Onat ) ),
% 0.99/1.64 hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.64 { ! class_Rings_Oring__1( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ),
% 0.99/1.64 c_Nat_Osemiring__1__class_Oof__nat( X, hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), Z ) ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), c_Nat_Osemiring__1__class_Oof__nat( X
% 0.99/1.64 , Y ) ), c_Nat_Osemiring__1__class_Oof__nat( X, Z ) ) }.
% 0.99/1.64 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) ) ) }.
% 0.99/1.64 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) ) ), hBOOL(
% 0.99/1.64 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 0.99/1.64 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ) ), Y ) ) }.
% 0.99/1.64 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ) ), Y ) ),
% 0.99/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 0.99/1.64 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.64 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) ) ) }.
% 0.99/1.64 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) ) ), hBOOL(
% 0.99/1.64 hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 0.99/1.64 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.64 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.64 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ) ), Y ) ) }.
% 0.99/1.64 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.64 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ) ), Y ) ),
% 0.99/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 0.99/1.64 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( X
% 0.99/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.99/1.64 c_Groups_Oone__class_Oone( X ) ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), Y ),
% 0.99/1.64 c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 0.99/1.64 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.99/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), U ), T ) ) ), hBOOL( hAPP( hAPP(
% 0.99/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), U ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ) ), T ) ) ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 0.99/1.64 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.99/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), U ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ) ), T ) ) ), hBOOL( hAPP(
% 0.99/1.64 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), U ), T ) ) ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 0.99/1.64 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.99/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), U ), T ) ) ), hBOOL( hAPP( hAPP(
% 0.99/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), U ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ) ), T ) ) ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 0.99/1.64 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.99/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), U ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ) ), T ) ) ), hBOOL( hAPP(
% 0.99/1.64 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), U ), T ) ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), hAPP( c_Nat_OSuc, Y )
% 0.99/1.64 ) ), X ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hAPP( c_Nat_OSuc,
% 0.99/1.64 hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), hAPP(
% 0.99/1.64 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = X }.
% 0.99/1.64 { ! hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 0.99/1.64 ), Y ), X ) ) ), ! alpha16( X, Y, Z ) }.
% 0.99/1.64 { ! hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 0.99/1.64 ), Y ), X ) ) ), ! alpha29( X, Y, Z ) }.
% 0.99/1.64 { alpha16( X, Y, Z ), alpha29( X, Y, Z ), hBOOL( hAPP( Z, hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.99/1.64 { ! alpha29( X, Y, Z ), ! hBOOL( hAPP( Z, skol26( T, U, Z ) ) ) }.
% 0.99/1.64 { ! alpha29( X, Y, Z ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.64 tc_Nat_Onat ), X ), skol26( X, Y, Z ) ) }.
% 0.99/1.64 { ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), T ),
% 0.99/1.64 hBOOL( hAPP( Z, T ) ), alpha29( X, Y, Z ) }.
% 0.99/1.64 { ! alpha16( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.64 tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.64 { ! alpha16( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.99/1.64 tc_Nat_Onat ) ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.64 hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha16(
% 0.99/1.64 X, Y, Z ) }.
% 0.99/1.64 { ! hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 0.99/1.64 ), Y ), X ) ) ), alpha17( X, Y, Z ) }.
% 0.99/1.64 { ! hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 0.99/1.64 ), Y ), X ) ) ), alpha30( X, Y, Z ) }.
% 0.99/1.64 { ! alpha17( X, Y, Z ), ! alpha30( X, Y, Z ), hBOOL( hAPP( Z, hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.99/1.64 { ! alpha30( X, Y, Z ), ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.64 tc_Nat_Onat ), X ), T ), hBOOL( hAPP( Z, T ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( Z, skol27( T, U, Z ) ) ), alpha30( X, Y, Z ) }.
% 0.99/1.64 { Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), skol27(
% 0.99/1.64 X, Y, Z ) ), alpha30( X, Y, Z ) }.
% 0.99/1.64 { ! alpha17( X, Y, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.64 tc_Nat_Onat, Y ), X ) ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.99/1.64 tc_Nat_Onat ) ) ) }.
% 0.99/1.64 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.64 alpha17( X, Y, Z ) }.
% 0.99/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha17
% 0.99/1.64 ( X, Y, Z ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP(
% 0.99/1.64 c_Nat_OSuc, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X )
% 0.99/1.64 , Y ) ) ), Z ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat )
% 0.99/1.64 , hAPP( c_Nat_OSuc, X ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.64 tc_Nat_Onat ), Y ), Z ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), hAPP(
% 0.99/1.64 c_Nat_OSuc, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X )
% 0.99/1.64 , Y ) ) ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ),
% 0.99/1.64 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP
% 0.99/1.64 ( c_Nat_OSuc, X ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ), hBOOL
% 0.99/1.64 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), T ) ), Z
% 0.99/1.64 ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), T ) ), Z
% 0.99/1.64 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) = hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), T ) ), Z
% 0.99/1.64 ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) = hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ), hAPP( hAPP
% 0.99/1.64 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), T ) = Z
% 0.99/1.64 }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), T ) = Z
% 0.99/1.64 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) = hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ), hBOOL
% 0.99/1.64 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), Z ) ) )
% 0.99/1.64 }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ),
% 0.99/1.64 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), Z ) ) )
% 0.99/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.64 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) = hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), T ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), Z ) ) }
% 0.99/1.64 .
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) = hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ), T = hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), Z ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP(
% 0.99/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), Z ),
% 0.99/1.64 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) = hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hAPP( c_Nat_OSuc,
% 0.99/1.64 hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ),
% 0.99/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), X = hAPP( c_Nat_OSuc
% 0.99/1.64 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ),
% 0.99/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.99/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = X }.
% 0.99/1.64 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = hAPP( c_Nat_OSuc,
% 0.99/1.64 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ),
% 0.99/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ), hBOOL
% 0.99/1.64 ( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), Z ) ) )
% 0.99/1.64 }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), Z ) ) )
% 0.99/1.64 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ), hBOOL
% 0.99/1.64 ( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), T ) ), Z
% 0.99/1.64 ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.64 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), T ) ), Z
% 0.99/1.64 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.64 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 0.99/1.64 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ) }.
% 0.99/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.64 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ),
% 0.99/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) ) }.
% 0.99/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.99/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.64 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.99/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ),
% 0.99/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__ring__1( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 0.99/1.64 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, hAPP(
% 0.99/1.64 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ), hAPP(
% 0.99/1.64 hAPP( c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, hAPP(
% 0.99/1.64 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP(
% 0.99/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 0.99/1.64 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.99/1.64 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.99/1.64 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.64 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.64 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.64 c_Power_Opower__class_Opower( X ), Y ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ),
% 0.99/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.64 { ! class_Groups_Omonoid__mult( X ), ! hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), hAPP( hAPP(
% 0.99/1.64 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Y ) ), Z
% 0.99/1.64 ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.64 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), Z ) ) ), T ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 0.99/1.64 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ) ),
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ) ),
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 0.99/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ) }.
% 0.99/1.64 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ) = hAPP
% 0.99/1.64 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP(
% 0.99/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) }.
% 0.99/1.64 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP(
% 0.99/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) = hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ) }.
% 0.99/1.64 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 0.99/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ),
% 0.99/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) = hAPP(
% 0.99/1.64 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__ring( X ), hAPP( hAPP( c_Polynomial_Osmult( X ), T )
% 0.99/1.64 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ),
% 0.99/1.64 Z ), Y ) ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z
% 0.99/1.64 ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Y ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), hAPP(
% 0.99/1.64 hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ) ) ), ! hBOOL
% 0.99/1.64 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ), hBOOL
% 0.99/1.64 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ),
% 0.99/1.64 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 0.99/1.64 ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__ab__semigroup__add( X ) }
% 0.99/1.64 .
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors( X ) }
% 0.99/1.64 .
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__semigroup__add( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Groups_Oab__semigroup__mult( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Groups_Ocomm__monoid__mult( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Groups_Oab__semigroup__add( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Groups_Ocomm__monoid__add( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring__1( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring__0( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Groups_Oab__group__add( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Rings_Ozero__neq__one( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Groups_Omonoid__mult( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__ring__1( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Groups_Omonoid__add( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Rings_Osemiring__1( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Rings_Osemiring__0( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Groups_Ogroup__add( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Rings_Omult__zero( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__ring( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Rings_Osemiring( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Groups_Ouminus( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Rings_Oring__1( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Groups_Ominus( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Power_Opower( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Groups_Ozero( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Rings_Oring( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Groups_Oone( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Rings_Odvd( X ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__comm__monoid__add( X ) }
% 0.99/1.64 .
% 0.99/1.64 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.99/1.64 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.99/1.64 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.99/1.64 ( tc_fun( Y, X ) ) }.
% 0.99/1.64 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.99/1.64 ) ) }.
% 0.99/1.64 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.99/1.64 .
% 0.99/1.64 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.99/1.64 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.99/1.64 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.99/1.64 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.64 tc_Int_Oint ) }.
% 0.99/1.64 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.64 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.99/1.64 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.64 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.99/1.64 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.99/1.64 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.99/1.64 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.99/1.64 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.99/1.64 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.99/1.64 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.99/1.64 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.99/1.64 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.99/1.64 { class_Nat_Osemiring__char__0( tc_Int_Oint ) }.
% 0.99/1.64 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.99/1.64 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.99/1.64 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.99/1.64 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.99/1.64 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Osemiring__1( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.99/1.64 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.99/1.64 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.99/1.64 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.99/1.64 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.99/1.64 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.99/1.64 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.99/1.64 { class_Power_Opower( tc_Int_Oint ) }.
% 0.99/1.64 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.99/1.64 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.99/1.64 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.99/1.64 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.64 tc_Nat_Onat ) }.
% 0.99/1.64 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Orderings_Owellorder( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Nat_Osemiring__char__0( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Rings_Osemiring__1( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.99/1.64 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.99/1.64 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.99/1.64 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.99/1.64 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.99/1.64 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.99/1.64 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ),
% 0.99/1.64 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.64 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.99/1.64 ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.64 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.99/1.64 X ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.64 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.99/1.64 ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.64 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.99/1.64 }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.64 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.64 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.64 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.64 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.99/1.64 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.64 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.64 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.64 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.64 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.64 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.99/1.64 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.99/1.64 ( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.99/1.64 ( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), class_Nat_Osemiring__char__0(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Osemiring__1(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.99/1.64 }.
% 0.99/1.64 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.99/1.64 ) ) }.
% 0.99/1.64 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.99/1.64 .
% 0.99/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.99/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.64 { hAPP( c_COMBI( Y ), X ) = X }.
% 0.99/1.64 { hAPP( hAPP( c_COMBK( T, Z ), Y ), X ) = Y }.
% 0.99/1.64 { hAPP( hAPP( hAPP( c_COMBB( W, U, T ), Z ), Y ), X ) = hAPP( Z, hAPP( Y, X
% 0.99/1.64 ) ) }.
% 0.99/1.64 { hAPP( hAPP( c_COMBC( W, U, T, Z ), Y ), X ) = hAPP( hAPP( Z, X ), Y ) }.
% 0.99/1.64 { hAPP( hAPP( hAPP( c_COMBS( W, U, T ), Z ), Y ), X ) = hAPP( hAPP( Z, X )
% 0.99/1.64 , hAPP( Y, X ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_fequal( Y ), X ) ), Y = X }.
% 0.99/1.64 { ! Y = X, hBOOL( hAPP( c_fequal( Y ), X ) ) }.
% 0.99/1.64 { ! hBOOL( c_fFalse ) }.
% 0.99/1.64 { ! hBOOL( hAPP( c_fNot, X ) ), ! hBOOL( X ) }.
% 0.99/1.64 { hBOOL( X ), hBOOL( hAPP( c_fNot, X ) ) }.
% 0.99/1.64 { ! hBOOL( X ), ! hBOOL( Y ), hBOOL( hAPP( hAPP( c_fconj, X ), Y ) ) }.
% 0.99/1.64 { ! hBOOL( hAPP( hAPP( c_fconj, X ), Y ) ), hBOOL( X ) }.
% 0.99/1.64 { ! hBOOL( hAPP( hAPP( c_fconj, Y ), X ) ), hBOOL( X ) }.
% 0.99/1.64 { ! hAPP( c_Polynomial_Opoly( t_a, hAPP( hAPP( c_Polynomial_OpCons( t_a ),
% 0.99/1.64 v_c____ ), v_cs____ ) ), v_x____ ) = hAPP( c_Polynomial_Opoly( t_a, hAPP
% 0.99/1.64 ( hAPP( c_Polynomial_OpCons( t_a ), v_c____ ), v_cs____ ) ), v_y____ ) }
% 0.99/1.64 .
% 0.99/1.64 { class_Rings_Oidom( t_a ) }.
% 0.99/1.64
% 0.99/1.64 *** allocated 15000 integers for clauses
% 0.99/1.64 *** allocated 22500 integers for clauses
% 0.99/1.64 *** allocated 33750 integers for clauses
% 0.99/1.64 *** allocated 50625 integers for clauses
% 0.99/1.64 *** allocated 75937 integers for clauses
% 0.99/1.64 percentage equality = 0.261229, percentage horn = 0.918285
% 0.99/1.64 This is a problem with some equality
% 0.99/1.64
% 0.99/1.64
% 0.99/1.64
% 0.99/1.64 Options Used:
% 0.99/1.64
% 0.99/1.64 useres = 1
% 0.99/1.64 useparamod = 1
% 0.99/1.64 useeqrefl = 1
% 0.99/1.64 useeqfact = 1
% 0.99/1.64 usefactor = 1
% 0.99/1.64 usesimpsplitting = 0
% 0.99/1.64 usesimpdemod = 5
% 0.99/1.64 usesimpres = 3
% 0.99/1.64
% 0.99/1.64 resimpinuse = 1000
% 0.99/1.64 resimpclauses = 20000
% 0.99/1.64 substype = eqrewr
% 0.99/1.64 backwardsubs = 1
% 0.99/1.64 selectoldest = 5
% 0.99/1.64
% 0.99/1.64 litorderings [0] = split
% 0.99/1.64 litorderings [1] = extend the termordering, first sorting on arguments
% 0.99/1.64
% 0.99/1.64 termordering = kbo
% 0.99/1.64
% 0.99/1.64 litapriori = 0
% 0.99/1.64 termapriori = 1
% 0.99/1.64 litaposteriori = 0
% 0.99/1.64 termaposteriori = 0
% 0.99/1.64 demodaposteriori = 0
% 0.99/1.64 ordereqreflfact = 0
% 0.99/1.64
% 0.99/1.64 litselect = negord
% 0.99/1.64
% 0.99/1.64 maxweight = 15
% 0.99/1.64 maxdepth = 30000
% 0.99/1.64 maxlength = 115
% 0.99/1.64 maxnrvars = 195
% 0.99/1.64 excuselevel = 1
% 0.99/1.64 increasemaxweight = 1
% 0.99/1.64
% 0.99/1.64 maxselected = 10000000
% 0.99/1.64 maxnrclauses = 10000000
% 0.99/1.64
% 0.99/1.64 showgenerated = 0
% 0.99/1.64 showkept = 0
% 0.99/1.64 showselected = 0
% 0.99/1.64 showdeleted = 0
% 0.99/1.64 showresimp = 1
% 0.99/1.64 showstatus = 2000
% 0.99/1.64
% 0.99/1.64 prologoutput = 0
% 0.99/1.64 nrgoals = 5000000
% 0.99/1.64 totalproof = 1
% 0.99/1.64
% 0.99/1.64 Symbols occurring in the translation:
% 0.99/1.64
% 0.99/1.64 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.99/1.64 . [1, 2] (w:1, o:221, a:1, s:1, b:0),
% 0.99/1.64 ! [4, 1] (w:0, o:121, a:1, s:1, b:0),
% 0.99/1.64 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.99/1.64 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.99/1.64 hAPP [38, 2] (w:1, o:245, a:1, s:1, b:0),
% 0.99/1.64 t_a [39, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.99/1.64 class_Rings_Oidom [40, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.99/1.64 v_p [41, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.99/1.64 c_Polynomial_Opoly [42, 2] (w:1, o:250, a:1, s:1, b:0),
% 0.99/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [43, 3] (w:1, o:
% 0.99/1.64 289, a:1, s:1, b:0),
% 0.99/1.64 c_Groups_Ozero__class_Ozero [45, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.99/1.64 v_cs____ [46, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.99/1.64 c_Polynomial_OpCons [47, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.99/1.64 v_c____ [48, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.99/1.64 class_Int_Oring__char__0 [52, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.99/1.64 class_Groups_Ozero [55, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.99/1.64 class_Rings_Ocomm__semiring__0 [60, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.99/1.64 c_Polynomial_Osynthetic__div [61, 3] (w:1, o:290, a:1, s:1, b:0),
% 0.99/1.64 c_Polynomial_Opcompose [64, 3] (w:1, o:292, a:1, s:1, b:0),
% 0.99/1.64 tc_Polynomial_Opoly [70, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.99/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [71, 3] (w:1
% 0.99/1.64 , o:293, a:1, s:1, b:0),
% 0.99/1.64 c_Groups_Oplus__class_Oplus [72, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.99/1.64 c_Groups_Otimes__class_Otimes [73, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.99/1.64 c_Polynomial_Osmult [74, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.99/1.64 class_Groups_Ocomm__monoid__add [75, 1] (w:1, o:155, a:1, s:1, b:0),
% 0.99/1.64
% 0.99/1.64 tc_fun [79, 2] (w:1, o:265, a:1, s:1, b:0),
% 0.99/1.64 c_COMBB [80, 3] (w:1, o:294, a:1, s:1, b:0),
% 0.99/1.64 c_COMBK [81, 2] (w:1, o:266, a:1, s:1, b:0),
% 0.99/1.64 c_COMBS [82, 3] (w:1, o:295, a:1, s:1, b:0),
% 0.99/1.64 c_Polynomial_Opoly__rec [83, 5] (w:1, o:328, a:1, s:1, b:0),
% 0.99/1.64 class_Rings_Olinordered__ring__strict [86, 1] (w:1, o:156, a:1, s:1
% 0.99/1.64 , b:0),
% 0.99/1.64 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [88
% 0.99/1.64 , 1] (w:1, o:183, a:1, s:1, b:0),
% 0.99/1.64 c_COMBC [89, 4] (w:1, o:318, a:1, s:1, b:0),
% 0.99/1.64 c_Polynomial_Oorder [90, 3] (w:1, o:291, a:1, s:1, b:0),
% 0.99/1.64 tc_Nat_Onat [91, 0] (w:1, o:58, a:1, s:1, b:0),
% 0.99/1.64 class_RealVector_Oreal__normed__algebra [93, 1] (w:1, o:157, a:1, s:1
% 0.99/1.64 , b:0),
% 0.99/1.64 class_Rings_Ocomm__semiring__1 [96, 1] (w:1, o:158, a:1, s:1, b:0),
% 0.99/1.64 class_Rings_Ocomm__semiring [100, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.99/1.64 c_If [106, 1] (w:1, o:184, a:1, s:1, b:0),
% 0.99/1.64 c_fequal [107, 1] (w:1, o:185, a:1, s:1, b:0),
% 0.99/1.64 class_Rings_Ono__zero__divisors [108, 1] (w:1, o:169, a:1, s:1, b:0)
% 0.99/1.64 ,
% 0.99/1.64 class_Rings_Oring__no__zero__divisors [109, 1] (w:1, o:170, a:1, s:1
% 0.99/1.64 , b:0),
% 0.99/1.64 class_Rings_Omult__zero [110, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.99/1.64 class_Rings_Osemiring [113, 1] (w:1, o:174, a:1, s:1, b:0),
% 0.99/1.64 class_Groups_Olinordered__ab__group__add [117, 1] (w:1, o:186, a:1
% 0.99/1.64 , s:1, b:0),
% 0.99/1.64 class_Groups_Omonoid__add [118, 1] (w:1, o:187, a:1, s:1, b:0),
% 0.99/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [119, 2] (w:1, o:
% 0.99/1.64 267, a:1, s:1, b:0),
% 0.99/1.64 c_Polynomial_Omonom [120, 3] (w:1, o:296, a:1, s:1, b:0),
% 0.99/1.64 c_Polynomial_OAbs__poly [121, 2] (w:1, o:268, a:1, s:1, b:0),
% 0.99/1.64 class_Rings_Ocomm__ring__1 [122, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.99/1.64 c_Groups_Ouminus__class_Ouminus [123, 1] (w:1, o:188, a:1, s:1, b:0)
% 0.99/1.64 ,
% 0.99/1.64 c_Groups_Oone__class_Oone [124, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.99/1.64 class_Rings_Oring__1__no__zero__divisors [125, 1] (w:1, o:171, a:1
% 0.99/1.64 , s:1, b:0),
% 0.99/1.64 class_Groups_Ogroup__add [126, 1] (w:1, o:189, a:1, s:1, b:0),
% 0.99/1.64 class_Groups_Oone [127, 1] (w:1, o:190, a:1, s:1, b:0),
% 0.99/1.64 class_Groups_Oab__group__add [130, 1] (w:1, o:191, a:1, s:1, b:0),
% 0.99/1.64 class_Rings_Ocomm__ring [131, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.99/1.64 class_Groups_Omonoid__mult [132, 1] (w:1, o:192, a:1, s:1, b:0),
% 0.99/1.64 class_Groups_Ocomm__monoid__mult [133, 1] (w:1, o:193, a:1, s:1, b:0)
% 0.99/1.64 ,
% 0.99/1.64 tc_HOL_Obool [135, 0] (w:1, o:81, a:1, s:1, b:0),
% 0.99/1.64 class_Rings_Oring [136, 1] (w:1, o:172, a:1, s:1, b:0),
% 0.99/1.64 class_Rings_Ozero__neq__one [137, 1] (w:1, o:175, a:1, s:1, b:0),
% 0.99/1.64 class_Groups_Oab__semigroup__mult [138, 1] (w:1, o:194, a:1, s:1, b:0
% 0.99/1.64 ),
% 0.99/1.64 class_Groups_Oab__semigroup__add [139, 1] (w:1, o:195, a:1, s:1, b:0)
% 0.99/1.64 ,
% 0.99/1.64 class_Groups_Ocancel__semigroup__add [140, 1] (w:1, o:196, a:1, s:1
% 0.99/1.64 , b:0),
% 0.99/1.64 class_Groups_Ocancel__ab__semigroup__add [141, 1] (w:1, o:197, a:1
% 0.99/1.64 , s:1, b:0),
% 0.99/1.64 c_Rings_Odvd__class_Odvd [142, 1] (w:1, o:198, a:1, s:1, b:0),
% 0.99/1.64 hBOOL [143, 1] (w:1, o:199, a:1, s:1, b:0),
% 0.99/1.64 c_Power_Opower__class_Opower [144, 1] (w:1, o:200, a:1, s:1, b:0),
% 0.99/1.64 class_Groups_Ouminus [146, 1] (w:1, o:201, a:1, s:1, b:0),
% 0.99/1.64 class_Rings_Olinordered__semiring__1 [150, 1] (w:1, o:161, a:1, s:1
% 0.99/1.64 , b:0),
% 0.99/1.64 c_Orderings_Oord__class_Oless__eq [151, 2] (w:1, o:247, a:1, s:1, b:0
% 0.99/1.64 ),
% 0.99/1.64 c_Polynomial_Ocoeff [152, 2] (w:1, o:269, a:1, s:1, b:0),
% 0.99/1.64 tc_Int_Oint [153, 0] (w:1, o:91, a:1, s:1, b:0),
% 0.99/1.64 class_Lattices_Oboolean__algebra [155, 1] (w:1, o:203, a:1, s:1, b:0)
% 0.99/1.64 ,
% 0.99/1.64 class_Rings_Odvd [157, 1] (w:1, o:176, a:1, s:1, b:0),
% 0.99/1.64 class_Groups_Oordered__ab__semigroup__add__imp__le [158, 1] (w:1, o:
% 0.99/1.64 204, a:1, s:1, b:0),
% 0.99/1.64 class_Groups_Oordered__ab__semigroup__add [159, 1] (w:1, o:205, a:1
% 0.99/1.64 , s:1, b:0),
% 0.99/1.64 class_Groups_Oordered__ab__group__add [160, 1] (w:1, o:206, a:1, s:1
% 1.66/1.99 , b:0),
% 1.66/1.99 class_Fields_Ofield [161, 1] (w:1, o:130, a:1, s:1, b:0),
% 1.66/1.99 class_Rings_Oordered__cancel__semiring [162, 1] (w:1, o:177, a:1, s:1
% 1.66/1.99 , b:0),
% 1.66/1.99 class_Rings_Oordered__ring [163, 1] (w:1, o:178, a:1, s:1, b:0),
% 1.66/1.99 class_Rings_Oordered__semiring [164, 1] (w:1, o:179, a:1, s:1, b:0),
% 1.66/1.99
% 1.66/1.99 class_Rings_Oordered__comm__semiring [165, 1] (w:1, o:180, a:1, s:1
% 1.66/1.99 , b:0),
% 1.66/1.99 class_Rings_Olinordered__ring [166, 1] (w:1, o:160, a:1, s:1, b:0),
% 1.66/1.99 class_Groups_Oordered__comm__monoid__add [167, 1] (w:1, o:207, a:1
% 1.66/1.99 , s:1, b:0),
% 1.66/1.99 class_Rings_Olinordered__semidom [168, 1] (w:1, o:162, a:1, s:1, b:0)
% 1.66/1.99 ,
% 1.66/1.99 class_Rings_Olinordered__idom [169, 1] (w:1, o:163, a:1, s:1, b:0),
% 1.66/1.99 class_Lattices_Oab__semigroup__idem__mult [170, 1] (w:1, o:202, a:1
% 1.66/1.99 , s:1, b:0),
% 1.66/1.99 class_Rings_Oring__1 [171, 1] (w:1, o:173, a:1, s:1, b:0),
% 1.66/1.99 class_Power_Opower [172, 1] (w:1, o:214, a:1, s:1, b:0),
% 1.66/1.99 class_Rings_Osemiring__0 [173, 1] (w:1, o:181, a:1, s:1, b:0),
% 1.66/1.99 class_Orderings_Opreorder [183, 1] (w:1, o:211, a:1, s:1, b:0),
% 1.66/1.99 c_Nat_OSuc [184, 0] (w:1, o:99, a:1, s:1, b:0),
% 1.66/1.99 c_Power_Opower_Opower [185, 3] (w:1, o:297, a:1, s:1, b:0),
% 1.66/1.99 class_Orderings_Olinorder [194, 1] (w:1, o:212, a:1, s:1, b:0),
% 1.66/1.99 class_Orderings_Oord [195, 1] (w:1, o:209, a:1, s:1, b:0),
% 1.66/1.99 class_Orderings_Oorder [196, 1] (w:1, o:210, a:1, s:1, b:0),
% 1.66/1.99 c_fNot [198, 0] (w:1, o:101, a:1, s:1, b:0),
% 1.66/1.99 c_Orderings_Oord__class_OLeast [199, 2] (w:1, o:248, a:1, s:1, b:0),
% 1.66/1.99
% 1.66/1.99 class_Orderings_Owellorder [200, 1] (w:1, o:213, a:1, s:1, b:0),
% 1.66/1.99 c_Nat_Onat_Onat__case [202, 3] (w:1, o:298, a:1, s:1, b:0),
% 1.66/1.99 c_fFalse [205, 0] (w:1, o:102, a:1, s:1, b:0),
% 1.66/1.99 c_Orderings_Oorder_Omono [206, 4] (w:1, o:321, a:1, s:1, b:0),
% 1.66/1.99 c_Int_Onat [208, 0] (w:1, o:104, a:1, s:1, b:0),
% 1.66/1.99 class_Rings_Olinordered__semiring__1__strict [209, 1] (w:1, o:164, a:
% 1.66/1.99 1, s:1, b:0),
% 1.66/1.99 c_Orderings_Oord__class_Oless [210, 2] (w:1, o:249, a:1, s:1, b:0),
% 1.66/1.99 class_Groups_Oordered__cancel__ab__semigroup__add [211, 1] (w:1, o:
% 1.66/1.99 215, a:1, s:1, b:0),
% 1.66/1.99 class_Rings_Olinordered__semiring__strict [213, 1] (w:1, o:165, a:1
% 1.66/1.99 , s:1, b:0),
% 1.66/1.99 class_Rings_Olinordered__comm__semiring__strict [214, 1] (w:1, o:166
% 1.66/1.99 , a:1, s:1, b:0),
% 1.66/1.99 class_Rings_Olinordered__semiring [219, 1] (w:1, o:167, a:1, s:1, b:0
% 1.66/1.99 ),
% 1.66/1.99 c_Int_Onat__aux [224, 2] (w:1, o:270, a:1, s:1, b:0),
% 1.66/1.99 c_Nat__Transfer_Otransfer__morphism [225, 4] (w:1, o:319, a:1, s:1
% 1.66/1.99 , b:0),
% 1.66/1.99 c_fconj [226, 0] (w:1, o:107, a:1, s:1, b:0),
% 1.66/1.99 c_Orderings_Oorder_Ostrict__mono [227, 4] (w:1, o:322, a:1, s:1, b:0)
% 1.66/1.99 ,
% 1.66/1.99 c_Polynomial_Opos__poly [228, 2] (w:1, o:271, a:1, s:1, b:0),
% 1.66/1.99 c_Nat_Osemiring__1__class_Oof__nat [230, 2] (w:1, o:246, a:1, s:1, b:
% 1.66/1.99 0),
% 1.66/1.99 class_Nat_Osemiring__char__0 [231, 1] (w:1, o:208, a:1, s:1, b:0),
% 1.66/1.99 class_Rings_Osemiring__1 [232, 1] (w:1, o:182, a:1, s:1, b:0),
% 1.66/1.99 c_Nat_Osemiring__1__class_Oof__nat__aux [233, 4] (w:1, o:320, a:1, s:
% 1.66/1.99 1, b:0),
% 1.66/1.99 c_Int_Oring__1__class_Oof__int [235, 2] (w:1, o:272, a:1, s:1, b:0),
% 1.66/1.99
% 1.66/1.99 c_Groups_Ominus__class_Ominus [236, 1] (w:1, o:216, a:1, s:1, b:0),
% 1.66/1.99 class_Groups_Ominus [240, 1] (w:1, o:217, a:1, s:1, b:0),
% 1.66/1.99 c_COMBI [241, 1] (w:1, o:218, a:1, s:1, b:0),
% 1.66/1.99 class_Groups_Ocancel__comm__monoid__add [246, 1] (w:1, o:219, a:1, s:
% 1.66/1.99 1, b:0),
% 1.66/1.99 v_x____ [256, 0] (w:1, o:119, a:1, s:1, b:0),
% 1.66/1.99 v_y____ [257, 0] (w:1, o:120, a:1, s:1, b:0),
% 1.66/1.99 alpha1 [258, 3] (w:1, o:299, a:1, s:1, b:1),
% 1.66/1.99 alpha2 [259, 3] (w:1, o:305, a:1, s:1, b:1),
% 1.66/1.99 alpha3 [260, 3] (w:1, o:307, a:1, s:1, b:1),
% 1.66/1.99 alpha4 [261, 2] (w:1, o:274, a:1, s:1, b:1),
% 1.66/1.99 alpha5 [262, 2] (w:1, o:275, a:1, s:1, b:1),
% 1.66/1.99 alpha6 [263, 2] (w:1, o:276, a:1, s:1, b:1),
% 1.66/1.99 alpha7 [264, 2] (w:1, o:277, a:1, s:1, b:1),
% 1.66/1.99 alpha8 [265, 4] (w:1, o:323, a:1, s:1, b:1),
% 1.66/1.99 alpha9 [266, 4] (w:1, o:324, a:1, s:1, b:1),
% 1.66/1.99 alpha10 [267, 2] (w:1, o:278, a:1, s:1, b:1),
% 1.66/1.99 alpha11 [268, 3] (w:1, o:300, a:1, s:1, b:1),
% 14.10/14.45 alpha12 [269, 2] (w:1, o:279, a:1, s:1, b:1),
% 14.10/14.45 alpha13 [270, 2] (w:1, o:280, a:1, s:1, b:1),
% 14.10/14.45 alpha14 [271, 2] (w:1, o:281, a:1, s:1, b:1),
% 14.10/14.45 alpha15 [272, 2] (w:1, o:282, a:1, s:1, b:1),
% 14.10/14.45 alpha16 [273, 3] (w:1, o:301, a:1, s:1, b:1),
% 14.10/14.45 alpha17 [274, 3] (w:1, o:302, a:1, s:1, b:1),
% 14.10/14.45 alpha18 [275, 3] (w:1, o:303, a:1, s:1, b:1),
% 14.10/14.45 alpha19 [276, 3] (w:1, o:304, a:1, s:1, b:1),
% 14.10/14.45 alpha20 [277, 4] (w:1, o:325, a:1, s:1, b:1),
% 14.10/14.45 alpha21 [278, 2] (w:1, o:283, a:1, s:1, b:1),
% 14.10/14.45 alpha22 [279, 2] (w:1, o:284, a:1, s:1, b:1),
% 14.10/14.45 alpha23 [280, 4] (w:1, o:326, a:1, s:1, b:1),
% 14.10/14.45 alpha24 [281, 4] (w:1, o:327, a:1, s:1, b:1),
% 14.10/14.45 alpha25 [282, 2] (w:1, o:285, a:1, s:1, b:1),
% 14.10/14.45 alpha26 [283, 2] (w:1, o:286, a:1, s:1, b:1),
% 14.10/14.45 alpha27 [284, 2] (w:1, o:287, a:1, s:1, b:1),
% 14.10/14.45 alpha28 [285, 2] (w:1, o:288, a:1, s:1, b:1),
% 14.10/14.45 alpha29 [286, 3] (w:1, o:306, a:1, s:1, b:1),
% 14.10/14.45 alpha30 [287, 3] (w:1, o:308, a:1, s:1, b:1),
% 14.10/14.45 alpha31 [288, 1] (w:1, o:220, a:1, s:1, b:1),
% 14.10/14.45 alpha32 [289, 2] (w:1, o:273, a:1, s:1, b:1),
% 14.10/14.45 alpha33 [290, 3] (w:1, o:309, a:1, s:1, b:1),
% 14.10/14.45 alpha34 [291, 3] (w:1, o:310, a:1, s:1, b:1),
% 14.10/14.45 skol1 [292, 2] (w:1, o:251, a:1, s:1, b:1),
% 14.10/14.45 skol2 [293, 1] (w:1, o:139, a:1, s:1, b:1),
% 14.10/14.45 skol3 [294, 2] (w:1, o:256, a:1, s:1, b:1),
% 14.10/14.45 skol4 [295, 0] (w:1, o:13, a:1, s:1, b:1),
% 14.10/14.45 skol5 [296, 1] (w:1, o:140, a:1, s:1, b:1),
% 14.10/14.45 skol6 [297, 3] (w:1, o:311, a:1, s:1, b:1),
% 14.10/14.45 skol7 [298, 3] (w:1, o:312, a:1, s:1, b:1),
% 14.10/14.45 skol8 [299, 3] (w:1, o:313, a:1, s:1, b:1),
% 14.10/14.45 skol9 [300, 2] (w:1, o:257, a:1, s:1, b:1),
% 14.10/14.45 skol10 [301, 2] (w:1, o:258, a:1, s:1, b:1),
% 14.10/14.45 skol11 [302, 1] (w:1, o:135, a:1, s:1, b:1),
% 14.10/14.45 skol12 [303, 1] (w:1, o:136, a:1, s:1, b:1),
% 14.10/14.45 skol13 [304, 1] (w:1, o:137, a:1, s:1, b:1),
% 14.10/14.45 skol14 [305, 2] (w:1, o:259, a:1, s:1, b:1),
% 14.10/14.45 skol15 [306, 2] (w:1, o:260, a:1, s:1, b:1),
% 14.10/14.45 skol16 [307, 2] (w:1, o:261, a:1, s:1, b:1),
% 14.10/14.45 skol17 [308, 2] (w:1, o:262, a:1, s:1, b:1),
% 14.10/14.45 skol18 [309, 2] (w:1, o:263, a:1, s:1, b:1),
% 14.10/14.45 skol19 [310, 1] (w:1, o:138, a:1, s:1, b:1),
% 14.10/14.45 skol20 [311, 1] (w:1, o:141, a:1, s:1, b:1),
% 14.10/14.45 skol21 [312, 2] (w:1, o:252, a:1, s:1, b:1),
% 14.10/14.45 skol22 [313, 2] (w:1, o:253, a:1, s:1, b:1),
% 14.10/14.45 skol23 [314, 1] (w:1, o:142, a:1, s:1, b:1),
% 14.10/14.45 skol24 [315, 1] (w:1, o:143, a:1, s:1, b:1),
% 14.10/14.45 skol25 [316, 2] (w:1, o:254, a:1, s:1, b:1),
% 14.10/14.45 skol26 [317, 3] (w:1, o:314, a:1, s:1, b:1),
% 14.10/14.45 skol27 [318, 3] (w:1, o:315, a:1, s:1, b:1),
% 14.10/14.45 skol28 [319, 1] (w:1, o:144, a:1, s:1, b:1),
% 14.10/14.45 skol29 [320, 2] (w:1, o:255, a:1, s:1, b:1),
% 14.10/14.45 skol30 [321, 1] (w:1, o:145, a:1, s:1, b:1),
% 14.10/14.45 skol31 [322, 3] (w:1, o:316, a:1, s:1, b:1),
% 14.10/14.45 skol32 [323, 1] (w:1, o:146, a:1, s:1, b:1),
% 14.10/14.45 skol33 [324, 1] (w:1, o:147, a:1, s:1, b:1),
% 14.10/14.45 skol34 [325, 1] (w:1, o:148, a:1, s:1, b:1),
% 14.10/14.45 skol35 [326, 1] (w:1, o:149, a:1, s:1, b:1),
% 14.10/14.45 skol36 [327, 2] (w:1, o:264, a:1, s:1, b:1),
% 14.10/14.45 skol37 [328, 3] (w:1, o:317, a:1, s:1, b:1).
% 14.10/14.45
% 14.10/14.45
% 14.10/14.45 Starting Search:
% 14.10/14.45
% 14.10/14.45 *** allocated 113905 integers for clauses
% 14.10/14.45 *** allocated 170857 integers for clauses
% 14.10/14.45 Resimplifying inuse:
% 14.10/14.45 Done
% 14.10/14.45
% 14.10/14.45
% 14.10/14.45 Intermediate Status:
% 14.10/14.45 Generated: 3725
% 14.10/14.45 Kept: 2048
% 14.10/14.45 Inuse: 48
% 14.10/14.45 Deleted: 3
% 14.10/14.45 Deletedinuse: 0
% 14.10/14.45
% 14.10/14.45 *** allocated 256285 integers for clauses
% 14.10/14.45 Resimplifying inuse:
% 14.10/14.45 Done
% 14.10/14.45
% 14.10/14.45 *** allocated 384427 integers for clauses
% 14.10/14.45 Resimplifying inuse:
% 14.10/14.45 Done
% 14.10/14.45
% 14.10/14.45
% 14.10/14.45 Intermediate Status:
% 14.10/14.45 Generated: 8605
% 14.10/14.45 Kept: 4106
% 14.10/14.45 Inuse: 190
% 14.10/14.45 Deleted: 6
% 14.10/14.45 Deletedinuse: 0
% 14.10/14.45
% 14.10/14.45 *** allocated 256285 integers for termspace/termends
% 14.10/14.45 Resimplifying inuse:
% 14.10/14.45 Done
% 14.10/14.45
% 14.10/14.45 Resimplifying inuse:
% 14.10/14.45 Done
% 14.10/14.45
% 14.10/14.45 *** allocated 576640 integers for clauses
% 14.10/14.45 *** allocated 384427 integers for termspace/termends
% 14.10/14.45
% 14.10/14.45 Intermediate Status:
% 14.10/14.45 Generated: 16602
% 14.10/14.45 Kept: 6477
% 14.10/14.45 Inuse: 255
% 14.10/14.45 Deleted: 6
% 14.10/14.45 Deletedinuse: 0
% 14.10/14.45
% 14.10/14.45 Resimplifying inuse:
% 14.10/14.45 Done
% 14.10/14.45
% 14.10/14.45 Resimplifying inuse:
% 14.10/14.45 Done
% 14.10/14.45
% 14.10/14.45 *** allocated 864960 integers for clauses
% 14.10/14.45
% 14.10/14.45 Intermediate Status:
% 14.10/14.45 Generated: 22793
% 14.10/14.45 Kept: 8685
% 41.26/41.60 Inuse: 280
% 41.26/41.60 Deleted: 6
% 41.26/41.60 Deletedinuse: 0
% 41.26/41.60
% 41.26/41.60 *** allocated 576640 integers for termspace/termends
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 38576
% 41.26/41.60 Kept: 11285
% 41.26/41.60 Inuse: 300
% 41.26/41.60 Deleted: 6
% 41.26/41.60 Deletedinuse: 0
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60 *** allocated 864960 integers for termspace/termends
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60 *** allocated 1297440 integers for clauses
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 46550
% 41.26/41.60 Kept: 13291
% 41.26/41.60 Inuse: 330
% 41.26/41.60 Deleted: 6
% 41.26/41.60 Deletedinuse: 0
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 68008
% 41.26/41.60 Kept: 15460
% 41.26/41.60 Inuse: 345
% 41.26/41.60 Deleted: 6
% 41.26/41.60 Deletedinuse: 0
% 41.26/41.60
% 41.26/41.60 *** allocated 1297440 integers for termspace/termends
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 82405
% 41.26/41.60 Kept: 17619
% 41.26/41.60 Inuse: 426
% 41.26/41.60 Deleted: 10
% 41.26/41.60 Deletedinuse: 0
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60 *** allocated 1946160 integers for clauses
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 105925
% 41.26/41.60 Kept: 20975
% 41.26/41.60 Inuse: 441
% 41.26/41.60 Deleted: 10
% 41.26/41.60 Deletedinuse: 0
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60 Resimplifying clauses:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 114781
% 41.26/41.60 Kept: 23870
% 41.26/41.60 Inuse: 486
% 41.26/41.60 Deleted: 157
% 41.26/41.60 Deletedinuse: 0
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60 *** allocated 1946160 integers for termspace/termends
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 123060
% 41.26/41.60 Kept: 26215
% 41.26/41.60 Inuse: 516
% 41.26/41.60 Deleted: 157
% 41.26/41.60 Deletedinuse: 0
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 130140
% 41.26/41.60 Kept: 28617
% 41.26/41.60 Inuse: 546
% 41.26/41.60 Deleted: 157
% 41.26/41.60 Deletedinuse: 0
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60 *** allocated 2919240 integers for clauses
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 143962
% 41.26/41.60 Kept: 32081
% 41.26/41.60 Inuse: 576
% 41.26/41.60 Deleted: 157
% 41.26/41.60 Deletedinuse: 0
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 149586
% 41.26/41.60 Kept: 34251
% 41.26/41.60 Inuse: 596
% 41.26/41.60 Deleted: 158
% 41.26/41.60 Deletedinuse: 1
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 160415
% 41.26/41.60 Kept: 37395
% 41.26/41.60 Inuse: 606
% 41.26/41.60 Deleted: 158
% 41.26/41.60 Deletedinuse: 1
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 168557
% 41.26/41.60 Kept: 39421
% 41.26/41.60 Inuse: 621
% 41.26/41.60 Deleted: 158
% 41.26/41.60 Deletedinuse: 1
% 41.26/41.60
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 175788
% 41.26/41.60 Kept: 41789
% 41.26/41.60 Inuse: 641
% 41.26/41.60 Deleted: 158
% 41.26/41.60 Deletedinuse: 1
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60 Resimplifying clauses:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 182224
% 41.26/41.60 Kept: 43926
% 41.26/41.60 Inuse: 656
% 41.26/41.60 Deleted: 301
% 41.26/41.60 Deletedinuse: 1
% 41.26/41.60
% 41.26/41.60 *** allocated 2919240 integers for termspace/termends
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 193125
% 41.26/41.60 Kept: 45935
% 41.26/41.60 Inuse: 698
% 41.26/41.60 Deleted: 301
% 41.26/41.60 Deletedinuse: 1
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60 *** allocated 4378860 integers for clauses
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 220791
% 41.26/41.60 Kept: 50156
% 41.26/41.60 Inuse: 726
% 41.26/41.60 Deleted: 301
% 41.26/41.60 Deletedinuse: 1
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 237869
% 41.26/41.60 Kept: 53268
% 41.26/41.60 Inuse: 771
% 41.26/41.60 Deleted: 301
% 41.26/41.60 Deletedinuse: 1
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 245383
% 41.26/41.60 Kept: 55389
% 41.26/41.60 Inuse: 791
% 41.26/41.60 Deleted: 301
% 41.26/41.60 Deletedinuse: 1
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 252927
% 41.26/41.60 Kept: 57428
% 41.26/41.60 Inuse: 811
% 41.26/41.60 Deleted: 301
% 41.26/41.60 Deletedinuse: 1
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 257394
% 41.26/41.60 Kept: 59441
% 41.26/41.60 Inuse: 817
% 41.26/41.60 Deleted: 301
% 41.26/41.60 Deletedinuse: 1
% 41.26/41.60
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 266681
% 41.26/41.60 Kept: 62428
% 41.26/41.60 Inuse: 841
% 41.26/41.60 Deleted: 301
% 41.26/41.60 Deletedinuse: 1
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60 Resimplifying clauses:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 278160
% 41.26/41.60 Kept: 64545
% 41.26/41.60 Inuse: 856
% 41.26/41.60 Deleted: 542
% 41.26/41.60 Deletedinuse: 2
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60 Resimplifying inuse:
% 41.26/41.60 Done
% 41.26/41.60
% 41.26/41.60
% 41.26/41.60 Intermediate Status:
% 41.26/41.60 Generated: 299325
% 41.26/41.60 Kept: 67666
% 87.85/88.25 Inuse: 876
% 87.85/88.25 Deleted: 542
% 87.85/88.25 Deletedinuse: 2
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25 *** allocated 4378860 integers for termspace/termends
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 309268
% 87.85/88.25 Kept: 70280
% 87.85/88.25 Inuse: 901
% 87.85/88.25 Deleted: 542
% 87.85/88.25 Deletedinuse: 2
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 321477
% 87.85/88.25 Kept: 72375
% 87.85/88.25 Inuse: 916
% 87.85/88.25 Deleted: 542
% 87.85/88.25 Deletedinuse: 2
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 339766
% 87.85/88.25 Kept: 76318
% 87.85/88.25 Inuse: 946
% 87.85/88.25 Deleted: 542
% 87.85/88.25 Deletedinuse: 2
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25 *** allocated 6568290 integers for clauses
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 350082
% 87.85/88.25 Kept: 78972
% 87.85/88.25 Inuse: 951
% 87.85/88.25 Deleted: 543
% 87.85/88.25 Deletedinuse: 3
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 361429
% 87.85/88.25 Kept: 81183
% 87.85/88.25 Inuse: 981
% 87.85/88.25 Deleted: 543
% 87.85/88.25 Deletedinuse: 3
% 87.85/88.25
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 367757
% 87.85/88.25 Kept: 83355
% 87.85/88.25 Inuse: 986
% 87.85/88.25 Deleted: 543
% 87.85/88.25 Deletedinuse: 3
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25 Resimplifying clauses:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 377444
% 87.85/88.25 Kept: 85415
% 87.85/88.25 Inuse: 1006
% 87.85/88.25 Deleted: 630
% 87.85/88.25 Deletedinuse: 3
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 388100
% 87.85/88.25 Kept: 87482
% 87.85/88.25 Inuse: 1031
% 87.85/88.25 Deleted: 630
% 87.85/88.25 Deletedinuse: 3
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 399733
% 87.85/88.25 Kept: 89614
% 87.85/88.25 Inuse: 1061
% 87.85/88.25 Deleted: 630
% 87.85/88.25 Deletedinuse: 3
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 409475
% 87.85/88.25 Kept: 92028
% 87.85/88.25 Inuse: 1081
% 87.85/88.25 Deleted: 630
% 87.85/88.25 Deletedinuse: 3
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 418272
% 87.85/88.25 Kept: 94219
% 87.85/88.25 Inuse: 1101
% 87.85/88.25 Deleted: 630
% 87.85/88.25 Deletedinuse: 3
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 425226
% 87.85/88.25 Kept: 96970
% 87.85/88.25 Inuse: 1110
% 87.85/88.25 Deleted: 630
% 87.85/88.25 Deletedinuse: 3
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 440261
% 87.85/88.25 Kept: 100964
% 87.85/88.25 Inuse: 1140
% 87.85/88.25 Deleted: 631
% 87.85/88.25 Deletedinuse: 3
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25 *** allocated 6568290 integers for termspace/termends
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 450338
% 87.85/88.25 Kept: 103675
% 87.85/88.25 Inuse: 1150
% 87.85/88.25 Deleted: 631
% 87.85/88.25 Deletedinuse: 3
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25 Resimplifying clauses:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 461293
% 87.85/88.25 Kept: 106645
% 87.85/88.25 Inuse: 1165
% 87.85/88.25 Deleted: 706
% 87.85/88.25 Deletedinuse: 3
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 469379
% 87.85/88.25 Kept: 108807
% 87.85/88.25 Inuse: 1170
% 87.85/88.25 Deleted: 706
% 87.85/88.25 Deletedinuse: 3
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 477400
% 87.85/88.25 Kept: 110915
% 87.85/88.25 Inuse: 1175
% 87.85/88.25 Deleted: 706
% 87.85/88.25 Deletedinuse: 3
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 486706
% 87.85/88.25 Kept: 113457
% 87.85/88.25 Inuse: 1195
% 87.85/88.25 Deleted: 706
% 87.85/88.25 Deletedinuse: 3
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 501859
% 87.85/88.25 Kept: 115501
% 87.85/88.25 Inuse: 1205
% 87.85/88.25 Deleted: 706
% 87.85/88.25 Deletedinuse: 3
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 509682
% 87.85/88.25 Kept: 117847
% 87.85/88.25 Inuse: 1220
% 87.85/88.25 Deleted: 706
% 87.85/88.25 Deletedinuse: 3
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 517388
% 87.85/88.25 Kept: 119987
% 87.85/88.25 Inuse: 1235
% 87.85/88.25 Deleted: 706
% 87.85/88.25 Deletedinuse: 3
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 524533
% 87.85/88.25 Kept: 122179
% 87.85/88.25 Inuse: 1265
% 87.85/88.25 Deleted: 706
% 87.85/88.25 Deletedinuse: 3
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25 Resimplifying clauses:
% 87.85/88.25 Done
% 87.85/88.25
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 531242
% 87.85/88.25 Kept: 124390
% 87.85/88.25 Inuse: 1295
% 87.85/88.25 Deleted: 866
% 87.85/88.25 Deletedinuse: 3
% 87.85/88.25
% 87.85/88.25
% 87.85/88.25 Intermediate Status:
% 87.85/88.25 Generated: 536049
% 87.85/88.25 Kept: 126966
% 87.85/88.25 Inuse: 1296
% 87.85/88.25 Deleted: 866
% 87.85/88.25 Deletedinuse: 3
% 87.85/88.25
% 87.85/88.25 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34 *** allocated 9852435 integers for clauses
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 543479
% 192.96/193.34 Kept: 129251
% 192.96/193.34 Inuse: 1329
% 192.96/193.34 Deleted: 867
% 192.96/193.34 Deletedinuse: 3
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 550671
% 192.96/193.34 Kept: 131377
% 192.96/193.34 Inuse: 1344
% 192.96/193.34 Deleted: 867
% 192.96/193.34 Deletedinuse: 3
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 562313
% 192.96/193.34 Kept: 133755
% 192.96/193.34 Inuse: 1349
% 192.96/193.34 Deleted: 867
% 192.96/193.34 Deletedinuse: 3
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 574080
% 192.96/193.34 Kept: 136136
% 192.96/193.34 Inuse: 1354
% 192.96/193.34 Deleted: 867
% 192.96/193.34 Deletedinuse: 3
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 584161
% 192.96/193.34 Kept: 138543
% 192.96/193.34 Inuse: 1374
% 192.96/193.34 Deleted: 867
% 192.96/193.34 Deletedinuse: 3
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 591256
% 192.96/193.34 Kept: 140857
% 192.96/193.34 Inuse: 1399
% 192.96/193.34 Deleted: 867
% 192.96/193.34 Deletedinuse: 3
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 597531
% 192.96/193.34 Kept: 142890
% 192.96/193.34 Inuse: 1419
% 192.96/193.34 Deleted: 867
% 192.96/193.34 Deletedinuse: 3
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34 Resimplifying clauses:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 605670
% 192.96/193.34 Kept: 144895
% 192.96/193.34 Inuse: 1447
% 192.96/193.34 Deleted: 1021
% 192.96/193.34 Deletedinuse: 3
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 620511
% 192.96/193.34 Kept: 148773
% 192.96/193.34 Inuse: 1449
% 192.96/193.34 Deleted: 1021
% 192.96/193.34 Deletedinuse: 3
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 635198
% 192.96/193.34 Kept: 152381
% 192.96/193.34 Inuse: 1469
% 192.96/193.34 Deleted: 1021
% 192.96/193.34 Deletedinuse: 3
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34 *** allocated 9852435 integers for termspace/termends
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 646343
% 192.96/193.34 Kept: 156206
% 192.96/193.34 Inuse: 1489
% 192.96/193.34 Deleted: 1021
% 192.96/193.34 Deletedinuse: 3
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 652416
% 192.96/193.34 Kept: 159279
% 192.96/193.34 Inuse: 1496
% 192.96/193.34 Deleted: 1021
% 192.96/193.34 Deletedinuse: 3
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 664430
% 192.96/193.34 Kept: 164443
% 192.96/193.34 Inuse: 1503
% 192.96/193.34 Deleted: 1022
% 192.96/193.34 Deletedinuse: 3
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34 Resimplifying clauses:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 671760
% 192.96/193.34 Kept: 169242
% 192.96/193.34 Inuse: 1508
% 192.96/193.34 Deleted: 1098
% 192.96/193.34 Deletedinuse: 3
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 682673
% 192.96/193.34 Kept: 172394
% 192.96/193.34 Inuse: 1518
% 192.96/193.34 Deleted: 1098
% 192.96/193.34 Deletedinuse: 3
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 693059
% 192.96/193.34 Kept: 175315
% 192.96/193.34 Inuse: 1523
% 192.96/193.34 Deleted: 1098
% 192.96/193.34 Deletedinuse: 3
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 703949
% 192.96/193.34 Kept: 178241
% 192.96/193.34 Inuse: 1538
% 192.96/193.34 Deleted: 1098
% 192.96/193.34 Deletedinuse: 3
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 724761
% 192.96/193.34 Kept: 182153
% 192.96/193.34 Inuse: 1558
% 192.96/193.34 Deleted: 1099
% 192.96/193.34 Deletedinuse: 4
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 740568
% 192.96/193.34 Kept: 186064
% 192.96/193.34 Inuse: 1578
% 192.96/193.34 Deleted: 1099
% 192.96/193.34 Deletedinuse: 4
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34 Resimplifying clauses:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 748800
% 192.96/193.34 Kept: 189239
% 192.96/193.34 Inuse: 1593
% 192.96/193.34 Deleted: 1306
% 192.96/193.34 Deletedinuse: 4
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 757693
% 192.96/193.34 Kept: 191408
% 192.96/193.34 Inuse: 1608
% 192.96/193.34 Deleted: 1306
% 192.96/193.34 Deletedinuse: 4
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 766476
% 192.96/193.34 Kept: 193973
% 192.96/193.34 Inuse: 1613
% 192.96/193.34 Deleted: 1306
% 192.96/193.34 Deletedinuse: 4
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 781670
% 192.96/193.34 Kept: 196718
% 192.96/193.34 Inuse: 1618
% 192.96/193.34 Deleted: 1306
% 192.96/193.34 Deletedinuse: 4
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 791815
% 192.96/193.34 Kept: 199089
% 192.96/193.34 Inuse: 1643
% 192.96/193.34 Deleted: 1306
% 192.96/193.34 Deletedinuse: 4
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34 Resimplifying inuse:
% 192.96/193.34 Done
% 192.96/193.34
% 192.96/193.34
% 192.96/193.34 Intermediate Status:
% 192.96/193.34 Generated: 798845
% 192.96/193.34 Kept: 201292
% 192.96/193.34 Inuse:Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------